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On extended eigenvalues and extended eigenvectors of truncated shift

Hasan Alkanjo (2013)

Concrete Operators

In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..

On products of some Toeplitz operators on polyanalytic Fock spaces

Irène Casseli (2020)

Czechoslovak Mathematical Journal

The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols f and g , we establish a necessary and sufficient condition for the boundedness of some Toeplitz products T f T g ¯ subjected to certain restriction on f and g . We also characterize this property in terms of the Berezin transform.

On some new sharp embedding theorems in minimal and pseudoconvex domains

Romi F. Shamoyan, Olivera R. Mihić (2016)

Czechoslovak Mathematical Journal

We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in ℂ n . Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are...

On some problems connected with diagonal map in some spaces of analytic functions

Romi Shamoyan (2008)

Mathematica Bohemica

For any holomorphic function f on the unit polydisk 𝔻 n we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag f ( z ) = f ( z , ... , z ) , and prove that the diagonal map Diag maps the space Q p , q , s ( 𝔻 n ) of the polydisk onto the space Q ^ p , s , n q ( 𝔻 ) of the unit disk.

On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...

On the characteristic properties of certain optimization problems in complex analysis

Józef Baranowicz, Leon Mikołajczyk (1995)

Banach Center Publications

We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.

On the diametral dimension of weighted spaces of analytic germs

Michael Langenbruch (2016)

Studia Mathematica

We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces S ¹ α and S ₁ α for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

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