פרופסור מרק ילין

פרופסור מרק ילין

Prof. Mark Elin

פרופסור מרק ילין
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Department
Mathematics
Research Interests

Complex Analysis and Dynamical Systems

RESEARCH COLLABORATION
2012  At the Department of Mathematics, University of Rome II Tor Vergata, Italy (with Professor F. Bracci)

Current Position
Professor
Contact Information
Email
mark_elin@braude.ac.il
Telephone
04-9086427
Office
EM410
Education
Ph.D.
(Physics and Mathematics) Institute of Physics, Siberian Branch of the Academy of Sciences of the USSR Dissertation: P-convexity and Hurwitz composition in multidimensional
M.Sc.
(Mathematics) Krasnoyarsk State University, (USSR) Dissertation: On Hurwitz composition in several complex variables
Academic Appointments

2013-present Professor, ORT Braude College, Karmiel, Israel
2007-2013 Associate Professor, ORT Braude College, Karmiel, Israel
2002-2007 Senior Lecturer, ORT Braude College, Karmiel, Israel
2001-2004 Adjunct lecturer, Technion, Haifa, Israel
1998-2002 Lecturer, ORT Braude College, Karmiel, Israel
1998 Research Fellow, Mathematics Department, Technion, Haifa, Israel
1990-1997 Associate Professor, Department of Calculus and Department of Mathematical Methods in Physical Sciences, Krasnoyarsk State Pedagogical University (Russia)
1988-1990 Senior Lecturer, Department of Higher Mathematics, Siberian Technological Institute, Krasnoyarsk (USSR)
1984-1987 Research Fellow, Institute of Physics, Siberian Branch of the Academy of Sciences of the USSR
1984-1986 Adjunct lecturer, Krasnoyarsk State University (Russia)
1983-1984 Lecturer, Department of Higher Mathematics, Siberian Technological Institute, Krasnoyarsk (USSR)

Teaching Experience
ORT BRAUDE COLLEGE
  • Undergraduate Courses:
    Calculus I - for engineer students and for math students
    Calculus II
    Linear Algebra
    Advanced Mathematics (Ordinary Differential Equations and Laplace Transform)
    Partial Differential Equations (new course in ORT Braude College)
    Complex Analysis - for engineer students and for math students
    Dynamical Systems

OTHER UNIVERSITIES
  • Graduate Courses:
    Krasnoyarsk State University:  
                 
    Special Courses on Analytic Functions of Several Complex Variables
    Krasnoyarsk State Pedagogical University:
    Functional Analysis,  
    Theory of Probability and Mathematical Statistics,
    Differential Equations

  • Undergraduate Courses:
    The Technion:

    Calculus 2,
    Partial Differentia Equations,
    Complex Analysis
    Siberian Technological Institute:            
    Analytic Geometry,
    Calculus I,
    Calculus II
    Krasnoyarsk State University:
    Complex Analysis
    Krasnoyarsk State Pedagogical University:  
    Calculus I,
    Calculus II



Academic and Professional Awards and Grants

2000   The Guastella fellowship for young researchers, SACTA-RASHI Fund  
2004   Award for Excellence, ORT Braude College
2005   Award for Excellence, ORT Braude College
2006   Award for Excellence, ORT Braude College
2007   Award for Excellence, ORT Braude College

MEMBERSHIP IN PROFESSIONAL SOCIETIES
Israel Mathematical Union
American Mathematical Society
European Mathematical Society


Professional Activities

2013 Chair of one of the sessions, International Conference on Complex Analysis and Related Topics, Lviv, Ukraine
2013 Chair of the Mathematics Session, The Ninth Interdisciplinary Research Conference of the ORT Braude College
2012-2013 Member of the Organizing Committee of the Sixth International  Conference on Complex Analysis and Dynamical Systems in honor of  60–th Birthday of Professor David Shoikhet, organized by ORT Braude College (Karmiel, Israel), Bar-Ilan University (Ramat Gan, Israel) and University of Miami (Florida, USA)
2011-2013 Member of the Award Committee for innovative suggestion box, ORT Braude College
2012 Co-organizer of the Satellite Thematic Session on Quasiconformal Mappings and Complex Dynamical Systems on the 6-th European Congress of Mathematics, Krakow, Poland
2008-2012 Head of the Mathematics Department of ORT Braude College
2011 Member of the Team for Academic Development, ORT Braude College
2011 Co-organizer (from the Israeli side) of the section on Geometric Function Theory, Israeli-Polish Mathematical Meeting organized by the Israel Mathematical Union (IMU) and the Polish Mathematical Society (PTM)
2010-2011 Member of the Organizing Committee of the Fifth International Conference on Complex Analysis and Dynamical Systems, organized  by ORT Braude College (Karmiel, Israel), Bar-Ilan University (Ramat Gan, Israel) and University of Miami (Florida, USA)
2010 Member of the Organizing Committee of the International Workshop on Open problems in Complex Dynamical Systems
2009 Chair of one of the sessions, International Conference on Infinite Particle Systems and Complex Systems V, Kazimierz Dolny, Poland  
2009 Team Leader for the improvement of auxiliary tutoring  
2008-2009 Member of the Organizing Committee of the International Conference on Complex Analysis and Dynamical Systems IV, organized by ORT Braude College (Karmiel, Israel), Bar-Ilan University (Ramat Gan, Israel) and the University of Miami (Florida, USA)
2008 Member of the Organizing Committee of the International Workshop on Open problems in Complex Analysis and Dynamical Systems
2008 Chair of the Mathematics Session, The Fourth Interdisciplinary   Research Conference of the ORT Braude College
2007 Chair of the Mathematics\Physics Session, The Third Interdisciplinary   Research Conference of the ORT Braude College
2006-2008 Member of the Research Committee, ORT Braude College
2005-2006 Member of the Organizing Committee of the Third International Conference on Complex Analysis and Dynamical Systems, organized by  ORT Braude College (Karmiel, Israel), Bar-Ilan University (Ramat Gan, Israel) and the Technion (Haifa, Israel), editor of the conference abstracts
2005 Chair of one of the sessions, International Conference on Computational Methods and Function Theory, Joensuu, Finland  
2005  Organizer of the mini-workshop on Open Problems in Geometric Function Theory which held in ORT Braude College (Karmiel) at 25.08.2005
2004-present   Treasurer of the Galilee Research Center for Applied Mathematics of ORT Braude College
2003 Member of the Organizing Committee of the Second International           Conference on Complex Analysis and Dynamical Systems in honor of  60–th Birthday of Professor Lawrence Zalcman, organized by ORT Braude College (Karmiel, Israel), Bar-Ilan University (Pamat-Gan, Israel) and  University of Potsdam (Germany)


Educational activities

2008-2012 Chair of the educational program for the degree B.Sc. in Applied   Mathematics, ORT Braude College (Karmiel, Israel)
2005-2006 Creating of the educational program for the degree B.Sc. in Applied   Mathematics, ORT Braude College (Karmiel, Israel)


Reviewing papers for
Electronic Journal of Differential Equations;
Contemporary Mathematics (Israel Mathematical Conferences Proceedings)
Proceedings of the London Mathematical Society
Rendiconti del Seminario Matematico di Padova
Complex Analysis and Operator Theory
Acta Mathematica Sinica
Journal of Fixed Point Theory and Application
Complex Variables and Elliptic Equations
Applied Mathematics and Computation
ISRN (International Scholarly Research Network) Mathematical Analysis Journal
Journal of Mathematical Analysis and Applications
SCIENCE CHINA Mathematics
Proceedings Mathematical Sciences
Annales Polonici Mathematici
Analysis and Mathematical Physics
Abstract and Applied Analysis
Indian Journal of Mathematics
Annales Universitatis Mariae Curie-Skłodowska

Participation in conferences
1984 The XIXth conference in Function Theory and Topology, Yalta, USSR
1985 The XXth conference in Function Theory and Topology, Yalta, USSR 
1986 The XIth All-Union school in Theory of Operators on Functional Spaces, Chelyabinsk, USSR
1987 The All-Union Conference in Complex Analysis and Mathematical Physics, Siberian Branch of Academy of Sciences of the USSR, Krasnoyarsk, USSR
1987 The VIth conference in Complex Analysis and Differential Equations, Chernogolovka, USSR
2000 Israel Mathematical Union Conference, Haifa, Israel
2000 The Third World Congress in Nonlinear Analysts, Catania, Italy
2001 Differential Equations and Complex Analysis, Karmiel, Israel         
2001 Computational Methods and Functional Theory, Aviero, Portugal
2002 Multidimensional Complex Analysis, Krasnoyarsk, Russia
2002 International Congress of Mathematics-2002, Satellite Conference “Complex Analysis”, Shanghai, China   
2003 International Conference on Fixed Point Theory and its Applications, Valencia, Spain
2005 Computational Methods and Function Theory, Joensuu, Finland
2005 XXth Nevanlinna Colloquium, Lausanne, Switzerland
2006 International Conference on Complex and Harmonic Analysis, Thessaloniki, Greece
2007 Workshop in Complex Analysis, Holon Academic Institute of Technology, Holon, Israel
2007 International Conference on Extremal Problems in Complex and Real Analysis, Moscow, Russia
2007 8-th International Conference on Fixed Point Theory and its Applications, Chiang Mai, Thailand
2008 INDAM Workshop on Holomorphic Iteration, Semigroups, and Loewner Chains, Rome, Italy
2009 International Conference on Complex Analysis and Related Topics V, Turku, Finland
2009 International Conference on Infinite Particle Systems and Complex Systems V, Kazimierz Dolny, Poland
2010 New Trends in Harmonic and Complex Analysis, Bremen, Germany 
2011 Workshop in Complex Analysis, Holon Academic Institute of Technology, Holon, Israel
2011 International Symposium on Geometric Function Theory and Applications, Cluj-Napoca, Romania
2011 Israeli-Polish Mathematical Meeting, Lodz, Poland
2012 Harmonic and Complex Analysis and its Applications, Puerto de la Cruz, Tenerife, Canary Islands, Spain
2012 Operator theory and operator algebras, Ben-Gurion University of the Negev, Beer-Sheva, Israel
2012 International Conference on Complex Analysis and Related Topics (The 13th   Romanian-Finnish Seminar), Ploieşti, Romania 
2012 6th European Congress of Mathematics, Satellite Thematic Session on Quasiconformal Mappings and Complex Dynamical Systems, Krakow,Poland
2013 Chair of one of the sessions, International Conference on Complex Analysis and Related Topics, Lviv, Ukraine    

Colloquium & Seminar Lectures
1982 Colloquium talk at the Krasnoyarsk University, USSR
1983 Colloquium talk at the Novosibirsk University, USSR
1985 Professor L. Aizenberg’s Seminar on Complex Analysis, Krasnoyarsk University, USSR
1986 Professor L. Aizenberg’s Seminar on Complex Analysis, Krasnoyarsk 
University, USSR
1987 Professor V. Ivanov’s Seminar, Sverdlovsk University, USSR
1989 Professor L. Aizenberg’s Seminar on Complex Analysis, Krasnoyarsk 
University, USSR
1990 Professor B. Levin’s Seminar on Complex Analysis, Kharkov University, USSR
1994 Seminar in Multidimensional Complex Analysis, Krasnoyarsk University, Russia
1996 Seminar in Multidimensional Complex Analysis, Krasnoyarsk University, Russia
1997 Seminar on Applied Mathematics, ORT Braude College, Karmiel, Israel
1999 Seminar on Applied Mathematics, ORT Braude College, Karmiel, Israel
2000 Seminar on Applied Mathematics, ORT Braude College, Karmiel, Israel
2004 Professor L. Zalcman’s Seminar, Bar Ilan University, Israel  
2004 Seminar on Applied Mathematics, ORT Braude College, Karmiel, Israel
2005 Professor S. Reich’s Seminar on Nonlinear Analysis, Technion, Israel 
2005 The First Interdisciplinary Research Conference of the ORT Braude College
2006 The Second Interdisciplinary Research Conference of the ORT Braude College
2010 Professor S. Reich’s Seminar on Nonlinear Analysis, Technion, Israel (two seminar’s lectures)
2011 The Seventh Interdisciplinary Research Conference of the ORT Braude College
2013 The Ninth Interdisciplinary Research Conference of the ORT Braude College

Publications
Refereed Papers
  1. M. Elin, Multidimensional analogue of Hurwitz composition, Izv. VUZ. Matem. 2  (1985), 22-27 (in Russian, English translation: Soviet Math. (Iz. VUZ) 29 (1985), 25-32).
  2. M. Elin, Multidimensional analogue of Hurwitz composition, "Multidimensional Complex Analysis", Krasnoyarsk, Institute of Physics, Siberian Branch of the Academy of Sciences of the USSR, 1985, 226-227 (in Russian).
  3. M. Elin, On epimorphism of convolution operator in convex domains in Cn, Sibirsk. Mat. Zh. 27 (1986), 201-203 (in Russian).
  4. M. Elin, Generalization of Hurwitz composition, Izv. VUZ. Matem., 10 (1988), 74-76 (in Russian, English translation: Soviet Math. (Iz. VUZ) 32 (1988), 114-117).
  5. M. Elin, On one type convexity in multidimensional complex analysis, All-Union Institute of Scientific Research and Technical Information (VINITI), 1991, No 244-v91, 28 p.  (in Russian)
  6. M. Elin, Multidimensional Hadamard composition, Sibirsk. Mat. Zh., 35 (1994), 1052-1057 (in Russian, English translation: Siberian Math. J. 35 (1994), 936-940).
  7. M. Elin, An acceleration method for the multiple power series of entire exponential type functions, Advances in Modeling & Analysis, A, AMCE Press, 19 (1994),  29-33. 
  8. M. Elin, On some classes of holomorphic functions connected with Hadamard product, "Complex Analysis and Differential Equations", Krasnoyarsk, 1997 (in Russian).
  9. D. Aharonov, M. Elin, S. Reich and D. Shoikhet, Parametric representation of semi-complete vector fields on the unit ball in Cn and in Hilbert space, Atti Acad. Naz. Lincei Cl. Sci. Fiz. Mat. Natur. Rend. Lincei (9) Mat. Appl. 10 (1999), 229-253. 
  10. M. Elin, S. Reich and D. Shoikhet, Asymptotic behavior of semigroups of holomorphic mappings, Progr. Nonlinear Differential Equations Appl., 42, Birkhauser, Basel, 2000, 249-258. 
  11. M. Elin, S. Reich and D. Shoikhet, Holomorphically accretive mappings and spiral-shaped functions of proper contractions, Nonlinear Analysis Forum, 5 (2000), 149-161.
  12. M. Elin, S. Reich and D. Shoikhet, A semigroup approach to the geometry of domains in complex Banach spaces, Nonlinear Analysis, 47 (2001), 3271-3280.
  13. M. Elin and D. Shoikhet, Dynamic extension of the Julia-Wolff-Carathèodory Theorem, Dynam. Systems Appl. 10 (2001), 421-438.
  14. M. Elin, S. Reich and D. Shoikhet, Dynamics of inequalities in geometric function theory, J .Inequal. Appl., 6 (2001), 651-664.
  15. M. Elin, L. Harris, S. Reich and D. Shoikhet, Evolution equations and geometric function theory in  -algebras, J. Nonlinear Convex Anal., 3 (2002), 81-121.
  16. M. Elin and D. Shoikhet, Univalent functions of proper contractions spirallike with respect to a boundary point, Multidimensional Complex Analysis, Krasnoyarsk, 2002, 28-36.
  17. M. Elin, S. Reich and D. Shoikhet, Asymptotic behavior of semigroups of ρ-non-expansive and holomorphic mappings on the Hilbert ball, Ann. Mat. Pura Appl. (4) 181 (2002), 501-526.
  18. M. Elin, V. Goryainov, S. Reich and D. Shoikhet, Fractional iteration and functional equations for functions analytic in the unit disk, Comput. Methods Funct. Theory 2 (2002), 353-366.
  19. D. Aharonov, M. Elin and D. Shoikhet, Spirallike functions with respect to a boundary point, Journ. Math.  Anal. Appl. 280 (2003), 17-29.
  20. M.Elin, D.Shoikhet and V. Volkovich, Semigroups of holomorphic mappings on the unit disk with a boundary fixed point, Intern. J. Pure Appl. Math. 12 (2004), 427-453. 
  21. M. Elin, S. Reich and D. Shoikhet, Complex Dynamical Systems and the Geometry of Domains in Banach Spaces, 2004. Dissertationes Math. (Rozprawy Mat.) 427 (2004), 62 pp. 
  22. M. Elin and D. Shoikhet, Semigroups with boundary fixed points on the unit Hilbert ball and spirallike mappings, in: Geometric Function Theory in Several Complex Variables, 82-117, World Sci. Publishing, River Edge, NJ, 2004.
  23. M. Elin, A. Goldvard, S. Reich and D. Shoikhet, Dynamics of spirallike functions, Complex analysis and Dynamical Systems, 41-57, Contemp. Math.  364, Amer. Math. Soc., Providence, RI, 2004.
  24. M. Elin and V. Khatskevich, Kœnigs embedding problem for operator affine mappings, Complex analysis and Dynamical Systems II, 113-120, Contemp. Math.  382, Amer. Math. Soc., Providence, RI, 2005.
  25. L. Aizenberg, M. Elin and D. Shoikhet, On the Rogosinski radius for holomorphic mappings and some its applications, Studia Math. 168 (2) (2005), 147-158.
  26. M. Elin and V. Khatskevich, Triangular plus-operators in Banach spaces: applications to the Kœnigs embedding problem, J. Nonlinear Convex Anal., 6 (2005), 173-185.
  27. M. Elin, Covering and distortion theorems for spirallike functions with respect to a boundary point, Intern. J. Pure Appl. Math. 28 (2006), 387-400. 
  28. M. Elin and D. Shoikhet, Angle distortion theorems for starlike and spirallike functions with respect to a boundary point, Intern. Journ. Math. Math. Sci., 2006, Article ID 81615, 1–13.
  29. M. Elin, M. Levenshtein, D. Shoikhet and R. Tauraso, Rigidity of holomorphic generators and one-parameter semigroups,  Dynam. Systems Appl. 16 (2007), 251-266.
  30. M. Elin, D. Shoikhet and L. Zalcman, A flower structure of backward flow invariant domains for semigroups, C. R. Acad. Sci. Paris, Ser. 1, Math. 346 (2008), 293-296. 
  31. M. Elin, D. Shoikhet and L. Zalcman, A flower structure of backward flow invariant domains for semigroups, Ann. Acad. Sci. Fenn. Math., 33 (2008), 3-34.
  32. M. Elin, S. Reich and D. Shoikhet, A Julia-Carathéodory theorem for hyperbolically monotone mappings in the Hilbert ball, Israel J. Math., 164 (2008), 397-411.
  33. M. Elin, S. Reich, D. Shoikhet and F. Yacobzon, Asymptotic behavior of one-parameter semigroups and rigidity of holomorphic generators, Compl. Anal. Oper. Theory, 2 (2008), 55-86.
  34. M. Elin, M. Levenshtein, S. Reich and D. Shoikhet, Two rigidity theorems for holomorphic generators of continuous semigroups, J. Nonlinear Convex Anal. 9 (2008), 59-64.
  35. M. Elin, D. Shoikhet and L. Zalcman, Controlled approximation for some classes of holomorphic functions, Complex analysis and Dynamical Systems III, 63-92, Contemp. Math. 455, Amer. Math. Soc., Providence, RI, 2008.
  36. M. Elin, M. Levenshtein, S. Reich and D. Shoikhet, A rigidity theorem for holomorphic generators on the Hilbert ball, Proc. AMS. 136 (2008), 4313-4320. 
  37. M. Elin, D. Shoikhet and F. Yacobzon, Linearization models for parabolic type semigroups, J. Nonlinear Convex Anal. 9 (2008), 205-214.
  38. M. Elin, M. Levenshtein, S. Reich and D. Shoikhet, Commuting semigroups of holomorphic mappings, Math. Scand. 103 (2008), 295-319.
  39. M. Elin, D. Khavinson, S. Reich and D. Shoikhet, Linearization models for parabolic dynamical systems via Abel's functional equation, Ann. Acad. Sci. Fenn. Math. 35 (2010), 439-472.
  40. M. Elin, Extension operators via semigroups, Journ. Math.  Anal. Appl. 377 (2011) 239-250.
  41. F. Bracci, M. Elin, and D. Shoikhet, Normal forms and linearization of holomorphic dilation type semigroups in several variables, J. Nonlinear Convex Anal. 12 (2011) 143-154. 
  42. M. Elin, D. Shoikhet and F. Yacobzon, A distortion theorem for functions convex in one direction, Compl. Anal. Oper. Theory, 5 (2011) 751–758.
  43. M. Elin and D. Shoikhet, Boundary behavior and rigidity of semigroups of holomorphic mappings, Analysis and Math. Physics, 1 (2011) 241-258.
  44. M. Elin, D. Shoikhet and N. Tarkhanov, Separation of boundary singularities for holomorphic generators, Annali di Matematica Pura ed Applicata, 190 (2011) 595-618.
  45. L.A. Harris, D. Shoikhet, M. Elin and S. Reich, Dynamics of self-maps of the unit disk, Appendix H, in: D.S. Alexander, F. Iavernaro, A. Rosa, Early Days in Complex Dynamics, American Math. Soc. & London Math. Soc., 2011, 307-312.
  46. M. Elin, M. Levenshtein, S. Reich and D. Shoikhet, Some inequalities for the horosphere function and hyperbolically nonexpansive mappings on the Hilbert ball, Contemporary Mathematics. Fundamental Directions, 45 (2012) 75-93 (in Russian).
  47. V. Bolotnikov, M. Elin and D. Shoikhet, Inequalities for angular derivatives and boundary interpolation, Analysis and Math. Physics, 3 (2013) 63-96.
Books

  1. M. Elin and D. Shoikhet, Linearization Models for Complex Dynamical Systems. Topics in univalent functions, functions equations and semigroup theory, Birkhäuser Basel, 2010, 300 pp.
  2. M. Elin, F. Jacobzon, M. Levenshtein and D. Shoikhet, The Schwarz Lemma. Rigidity and Dynamics (117 pp.), chapter in: Harmonic and Complex Analysis and Applications, Birkhäuser Basel (accepted for publ.).


 

Conference Proceedings and Abstracts

  1. M. Elin, "Extension" of Szego kernels and generalization of linear convexity, XI All-Union school on operator theory on functional  paces, v.2, Chelyabinsk, 1986, p.43 (in Russian)
  2. M. Elin, Some properties of linear convexity, "Complex Analysis and Mathematical Physics", Krasnoyarsk, 1987, p. 30 (in Russian).
  3. M. Elin, On one type of convexity in multidimensional complex analysis, "Complex Analysis and Mathematical Physics", Krasnoyarsk, 1987, p.31 (in Russian)
  4. M. Elin, Uniqueness sets for one class of entire functions, "Actual problems of complex analysis", Tashkent, 1989 (in Russian).
  5. M. Elin and N. Kelberg, On integral means theorem, "Youth, Science and Third Thousand", Krasnoyarsk, 1996, pp. 24-25 (in Russian).
  6. M. Elin, M. Levenshtein, S. Reich and D. Shoikhet, Rigidity results for holomorphic mappings on the unit disk, in: Complex and Harmonic Analysis, Proceedings of the International Conference, Thessaloniki, 2006, 93-110, DEStech Publications, Inc., 2007.
  7. M. Elin, S. Reich, D. Shoikhet and F. Yacobzon, Rates of convergence of one-parameter semigroups with boundary Denjoy-Wolff fixed points, in: Fixed Point Theory and its Applications, Proceedings of the Eighth International Conference, Chiang Mai, Thailand, 2007, 43-58, Yokohama Publishers, 2008.


Other Publications
Ph.D. Thesis
P-convexity and Hurwitz composition in multidimensional complex analysis, Krasnoyarsk, 1987, 94pp.

Accepted for publication
  1. M. Elin and M. Levenshtein, Covering results and perturbed Roper-Suffridge operators, Compl. Anal. Oper. Theory, preprint is available in: arXiv:1202.3063

Unpublished Professional Reports (self-performed or supervised)
  1. M. Elin, Biholomorphic mappings and semigroup theory in multidimensional complex spaces, Research project, 1999.
  2. M. Elin and V.Khatskevich, Operator theory in spaces with indefinite metrics, holomorphic mappings in Banach spaces, and their application, Joint research project, 1999.  
  3. M. Elin and V. Khatskevich, Indefinite metric spaces theory, biholomorphisms and continuous semigroups in Banach spaces, Joint research project, 2003.
  4. M. Elin and V. Khatskevich, Indefinite metrics, continuous semigroups and biholomorphic mappings in Banach spaces, Joint research project, 2004.
  5. M. Agranovsky, M. Elin, Y. Kondratiev, O. Kutovyi, M. Levenshtein, T. Pasurek, M. Roeckner and D. Shoikhet, Evolutional equations in spaces of holomorphic functions, Joint research project, 2011.