On distinguished representative domains
Stefan Bergman (1977)
Annales Polonici Mathematici
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Stefan Bergman (1977)
Annales Polonici Mathematici
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Väisälä, Jussi (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Nikolai Nikolov (2006)
Annales Polonici Mathematici
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We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
Armen Edigarian (2004)
Annales Polonici Mathematici
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We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.
Meerschaert, M.M., Scheffler, H.-P. (1996)
Journal of Applied Analysis
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V. Barucci, D.E. Dobbs, M. Fontana (1986)
Manuscripta mathematica
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Karol Borsuk (1972)
Colloquium Mathematicae
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Ahmed Ayache, Hanen Monceur (2011)
Colloquium Mathematicae
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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.
Peter Pflug, Włodzimierz Zwonek (1998)
Annales Polonici Mathematici
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We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Włodzimierz Zwonek
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Our work is divided into five chapters. In Chapter I we introduce necessary notions and we present the most important facts that we shall use. We also present our main results. Chapter I covers the following topics: • holomorphically contractible families of functions and pseudometrics, their basic properties, product property, Lempert Theorem, notion of geodesic, problem of finding effective formulas for invariant functions and pseudometrics and geodesics, completeness...
Magdalena Gregorczyk, Leopold Koczan (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this article we take over methods for determination of Koebe set based on extremal sets for a given class of functions.
Klas Diederich, John Erik Fornaess (1978)
Manuscripta mathematica
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Edgar Lee Stout (2009)
Annales Polonici Mathematici
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We construct some envelopes of holomorphy that are not equivalent to domains in ℂⁿ.
Brian D. Sleeman, Chen Hua (2000)
Revista Matemática Iberoamericana
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A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries...
Armen Edigarian (2015)
Annales Polonici Mathematici
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We give a necessary and sufficient condition for the existence of a weak peak function by using Jensen type measures. We also show the existence of a weak peak function for a class of Reinhardt domains.
Alain Bouvier (1980)
Publications du Département de mathématiques (Lyon)
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McCasland, R.L., Moore, Marion E. (1991)
Portugaliae mathematica
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Herron, David A., Koskela, Pekka (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Peter Pflug, Włodzimierz Zwonek (1998)
Annales Polonici Mathematici
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Alessandro Monguzzi (2016)
Concrete Operators
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In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting...