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Spectra of subnormal Hardy type operators

K. Rudol (1997)

Annales Polonici Mathematici

The essential spectrum of bundle shifts over Parreau-Widom domains is studied. Such shifts are models for subnormal operators of special (Hardy) type considered earlier in [AD], [R1] and [R2]. By relating a subnormal operator to the fiber of the maximal ideal space, an application to cluster values of bounded analytic functions is obtained.

Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher, Hartmut Wolf (1997)

Banach Center Publications

Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk N or on the Segal-Bargmann space over N . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression A n of A to the linear span of the monomials z 1 k 1 . . . z N k N : 0 k j n . Unfortunately, in general the spectrum of A n does not mimic the spectrum of A as...

Spectral study of holomorphic functions with bounded growth

Ivan Cnop (1972)

Annales de l'institut Fourier

This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables.The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.

Spectrum of certain Banach algebras and ∂̅-problems

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

Annales Polonici Mathematici

We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.

Steinness of bundles with fiber a Reinhardt bounded domain

Karl Oeljeklaus, Dan Zaffran (2006)

Bulletin de la Société Mathématique de France

Let E denote a holomorphic bundle with fiber D and with basis B . Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3 , we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1 ); for d = 2 , we give necessary and sufficient criteria for E to be Stein (Theorem 2 ). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem 3 ).

Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang (2014)

Annales Polonici Mathematici

Let A ζ = Ω - ρ ( ζ ) · Ω ¯ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel K ζ ( z ) of A ζ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that A ζ is non-pseudoconvex when the dimension of A ζ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for ² l o g K ζ / ζ ζ ̅ , as well as its boundary behavior.

Strong boundary values : independence of the defining function and spaces of test functions

Jean-Pierre Rosay, Edgar Lee Stout (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.

Structure of spaces of germs of holomorphic functions.

Nguyen Van Khue, P. Thien Danh (1997)

Publicacions Matemàtiques

Let E be a Frechet (resp. Frechet-Hilbert) space. It is shown that E ∈ (Ω) (resp. E ∈ (DN)) if and only if [H(OE)]' ∈ (Ω) (resp. [H(OE)]' ∈ (DN)). Moreover it is also shown that E ∈ (DN) if and only if Hb(E') ∈ (DN). In the nuclear case these results were proved by Meise and Vogt [2].

Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd (2001)

Commentationes Mathematicae Universitatis Carolinae

Polynomials on n with values in an irreducible Spin n -module form a natural representation space for the group Spin n . These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on n with values in these modules.

Su alcune formule integrali per le funzioni di più variabili complesse

Guido Lupacciolu (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

General topological conditions are given for integration cycles of a certain class of integral formulas for holomorphic functions of several complex variables.

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