A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions

Jarnicki, Marek

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Tytuł książki

A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions

Autorzy

Marek Jarnicki

Seria

Rozprawy Matematyczne tom/nr w serii: 258 wydano: 1987

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Abstrakty

CONTENTS
§1. Introduction.................................................................................................................5
§2. Basic properties of δ-tempered holomorphic functions...............................................8
§3. Holomorphic continuation and holomorphic retractions.............................................20
§4. Continuation from regular neighbourhoods...............................................................32
§5. Continuation from δ-regular submanifolds; Main Theorem........................................35
§6. Holomorphic retractions and pseudoinverse matrices; proof of Main Theorem.........39
References.....................................................................................................................49

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 258

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCLVIII

Daty

wydano

1987

Twórcy

autor

Marek Jarnicki

Bibliografia

[1] I. Cnop, Extending holomorphic functions with bounded growth from certain graphs, Value Distribution Theory, M. Dekker, 1975.
[2] J.-P. Demailly, Scindage holomorphe d'un morphisme de fibres vectoriels semi-positifs avec estimations $L^2$, Seminaire P. Lelong - H. Skoda (Analyse), 20e et 21e année, 1980-1981, Lect. Notes in Math. 919.
[3] J.-P. Ferrier, Spectral Theory and Complex Analysis, North-Holland Publishing Company, Amsterdam-London 1973.
[4] R. Gunning, H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, Inc.. Englewoof Cliffs, N. J., 1965.
[5] W. Hayman, Interpolation by bounded functions, Ann. Inst. Fourier 8 (1958), 277-290.
[6] L. Hörmander, Generators for some rings of analytic functions, Bull. Amer. Math. Soc. 73 (1967), 943-949.
[7] L. Hörmander, An Introduction to Complex Analysis in Several Variables, North-Holland Publishing Company, Amsterdam-London 1973.
[8] M. Jarnicki, Holomorphic functions with bounded growth on Riemann domains over C, Z. Nauk. UJ 20 (1979), 43-51.
[9] M. Jarnicki, Holomorphic Functions with Bounded Growth on Riemann Domains over O, Bull. Acad. Sci. Pol. 27 (9) (1979), 675-680.
[10] M. Jarnicki, Holomorphic functions with restricted growth on complex manifolds, Z. Nauk. UJ 22 (1981), 85-93.
[11] M. Jarnicki, Holomorphic continuation of functions with restricted growth, ibid. 23 (1982), 7-14.
[12] M. Jarnicki, Homomorphic continuation of holomorphic functions with bounded growth, Univ. Iag. Acta Math. 24 (1984), 209-216.
[13] M. Jarnicki, Holomorphic continuation with restricted growth, ibid. 25 (1985), 133-143.
[14] M. Jarnicki, Multiplicative linear functionals on some algebras of holomorphic functions with restricted growth, Ann. Pol. Math. 44 (1984), 353-361.
[15] M. Jarnicki, A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of S-tempered functions, Preprint 276 of the Polish Academy of Sciences 1983.
[16] B. Jennane, Extension d'une fonction définie sur une sous-variété avec contrôle de la croissance, Lect. Notes in Math. 694, 126-133.
[17] J. J. Kelleher, B. A. Taylor, Finitely generated ideals in rings of analytic functions, Math. Ann. 193 (1971), 225-237.
[18] F. Leja, Theory of Analytic Functions, PWN, Warszawa 1957 (in Polish).
[19] A. F. Leontiev, On the interpolation in the class of entire functions of finite order, Doklady Akademii Nauk S.S.S.R. 61 (1948), 785-787 (in Russian).
[20] P. Mazet, M. Jarnicki, A note on holomorphic continuation with restricted growth, Univ. Iag. Acta Math. 25 (1985), 145-147.
[21] J. R. Narasimhan, Cohomology with bounds on complex spaces, Lect. Notes in Math. 155, 141-150.
[22] Y. Nishimura, Problème d'extension dans le théorie des fonctions entières d'ordre fini, J. Math. Kyoto Univ. 20 (4) (1980), 635-650.
[23] H. Rossi, J. L. Taylor, On Algebras of Holomorphic Functions on Finite Pseudoconvex Manifolds, J. Funct. Analysis 24 (1) (1977), 11-31.

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bwmeta1.element.zamlynska-87026923-1b28-4f8a-af87-5ad0e0a8d3f3

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83-01-07374-8

ISSN

0012-3862

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