Analytic functionals and Bergman spaces

Zorn, Paul

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 9 (1982) no. 3, pp. 365-404.

[1] S.S. Abhyankar, Local Analytic Geometry, Academic Press, New York, 1964. | MR | Zbl

[2] L.A. Aizenberg, The general form of a linear continuous functional in spaces of functions that are holomorphic in convex domains of CN, Soviet Math., 7 (1966), pp. 198-201. | Zbl

[3] S.R. Bell, A representation theorem in strictly pseudo convex domains, to appear. | Zbl

[4] S.R. Bell, Biholomorphic mappings and the ∂-Problem, Ann. Math., 114 (1981), pp. 103-113. | Zbl

[5] S.R. Bell, Nonvanishing of the Bergman kernel function at boundary points of certain domains in CN, Math. Ann., 244 (1979), pp. 69-74. | EuDML | MR | Zbl

[6] S. Bergman, The Kernel Function and Conformal Mapping, 2nd ed., Amer. Math. Soc., Providence, 1970. | MR | Zbl

[7] M. Derridj - D. Tartakoff, On global real-analyticity of solutions to the ∂-Neumann problem, Comm. Partial Diff. Equat., 1 (1976), pp. 401-435. | Zbl

[8] R.E. Edwards, Functional Analysis, Holt, Rinehart, and Winston, New York, 1965. | MR | Zbl

[9] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math., 26 (1974), pp. 1-65. | EuDML | MR | Zbl

[10] G.B. Folland - J.J. Kohn, The Neumann Problem for the Cauchy-Riemann Complex, Princeton University Press, Princeton, 1972. | MR | Zbl

[11] B.A. Fuks, Special Chapters in the Theory of Analytic Functions of Several Complex Variables, Amer. Math. Soc., Providence, Rhode Island, 1965. | MR | Zbl

[12] I.M. Gelfand - G.E. Shilov, Generalized Functions, vol. II, Academic Press, New York, 1968. | MR | Zbl

[13] G.M. Goluzin, Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence, 1969. | MR | Zbl

[14] P. Griffiths - J. Harris, Principles of Algebraic Geometry, John Wiley and Sons, New York, 1978. | MR | Zbl

[15] A. Grothendieck, Sur certains espaces de fonctions holomorphes, J. Reine Angew. Math., 192 (1953), pp. 35-64. | MR | Zbl

[16] G.M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains, and some applications, Math. USSR-Sb., 7 (1969), pp. 597-616. | Zbl

[17] G.M. Henkin - E.M. Čirka, Boundary properties of holomorphic functions of several complex variables, J. Soviet Math., 5 (1976), pp. 612-687. | MR | Zbl

[18] L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966. | MR | Zbl

[19] N Kerzman, Differentiability at the boundary of the Bergman kernel function, Math. Ann., 195 (1972), pp. 149-158. | MR

[20] N. Kerzman, Hölder and Lp estimates for solutions of ∂u = f in strongly pseudo- convex domains, Comm. Pure Appl. Math., 24 (1971), pp. 301-380. | Zbl

[21] C.O. Kiselman, On unique supports of analytic functionals, Ark. Mat., 6 (1965), pp. 307-318. | MR | Zbl

[22] J.J. Kohn, Harmonic integrals on strictly pseudoconvex manifolds, I, Ann. of Math., 781 (1963), pp. 112-148. | MR | Zbl

[23] G. Komatsu, Global analytic-hypoellipticity of the ∂-Neumann problem, Tôhoku Math. J., 28 (1976), pp. 145-156. | Zbl

[24] G. Köthe, Über zwei Sätze von Banach, Math. Z., 53 (1950), pp. 203-209. | MR | Zbl

[25] P. Lelong, Fonctionnelles analytiques et fonctions entières (n variables), les Presses de l'Université de Montréal, Montréal, 1968. | MR | Zbl

[26] A. Martineau, Sur la topologie des espaces de fonctions holomorphes, Math. Ann., 163 (1966), pp. 62-88. | MR | Zbl

[27] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math., 11 (1963), pp. 1-64. | MR | Zbl

[28] L. Nirfnbfrg - S. Webster - P. Yang, Local boundary regularity of holomorphic mappings, Comm. Pure Appl. Math., 33 (1980), pp. 305-338. | MR | Zbl

[29] S.I. Pin, On the analytic continuation of holomorphic mappings, Math. USSR-Sb., 27 (1975), pp. 375-392. | MR | Zbl

[30] R. Sulanke - P. Wintgen, Differentialgeometrie und Faserbündel, Birkhäuser verlag, Basel, 1972. | MR | Zbl

[31] D.S. Tartakoff, The local real analyticity of solutions to □ b and the ∂-Neumann problem, Acta Math., 145 (1980), pp. 177-204. | Zbl

[32] G. Tomassini, Tracce delle funzioni olomorfe sulle sottovarietà analitiche reali d'una varietà complessa, Ann. Scuola Norm. Sup. Pisa, 20 (1966), pp. 31-43. | Numdam | MR | Zbl

[33] F. Treves, Analytic hypoellipticity of a class of pseudodifferential operators with double characteristics and applications to the ∂-Neumann problem, Comm. Partial Diff. Equat., 3 (1978), pp. 475-642. | Zbl

[34] S.E. Warschawski, On differentiability at the boundary of conformal mappings, Proc. Amer. Math. Soc., 12 (1961), pp. 614-620. | MR | Zbl

[35] K. Yosida, Functional Analysis, 4th ed., Springer-Verlag, New York, 1974. | MR | Zbl

[36] S.V. Znamenskii, A geometric criterion for strong linear convexity, Functional Anal. Appl., 13 (1979), pp. 224-225. | MR | Zbl