International Congress Series

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ISSN: 05315131

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International Congress Series

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Publications found: 1443

Springer Nature

The $$ \mathbb{C}^{\textit{n}} $$ n case

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

In view of the tensor product decomposition (8.0.2), we are in the setting of Subsection 7.3.

Springer Nature

Basis-oriented approach

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

Other examples are given, e.g., in the recent papers [13, 24, 25, 29, 30, 31, 37], where non-standardly-weighted spaces related to analytic functions are considered.

Springer Nature

The unit ball $$ \mathbb{B}^{\textit{n}} $$ n case

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

Here we follow the approach of Section 8.3, but take into account the differences between this case and the one considered therein.

Springer Nature

Upper half-plane Π case

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

Between the descriptions of the polyanalytic type spaces in L2( $$ \mathbb{D} $$ ) and in L2(Π) there is an essential difference.

Springer Nature

Extended Fock-space construction approach

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

We will deal with functions defined in a connected simply connected domain D ⊂ $$ \mathbb{C} $$ . Among the typical examples considered in what follows are the unit disk $$ \mathbb{D} $$ and the entire plane $$ \mathbb{C} $$ .

Springer Nature

Approach based on pure isometries

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

The next proposition collects a number of obvious properties of Wm,n and of objects related to Wm,n.

Springer Nature

The Siegel domain case

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

In the subsequent two sections we present two different characterizations of polyanalytic subspaces on the Siegel domain.

Springer Nature

Unit disk $$ \mathbb{D} $$ case

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

The rigid motions of the unit disk $$ \mathbb{D} $$ , regarded as the hyperbolic plane, are given by the Möbius transformations.

Springer Nature

Multi-operator extended Fock-space construction

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

In what follows we will consider connected simply connected domains D ⊂ $$ \mathbb{C} $$ n (the typical examples are the unit ball $$ \mathbb{B} $$ n and the whole space $$ \mathbb{C} $$ n).

Springer Nature

Hilbert spaces with generalized Gaussian measure on $$ \mathbb{C} $$ 2

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

In this chapter, we consider Hilbert spaces with a generalized Gaussian measure in the several-variable case. To simplify the presentation, we restrict the discussion to the case of only two complex variables, i.e., spaces over $$ \mathbb{C} $$ 2.

Springer Nature

Complex plane $$ \mathbb{C} $$ case

Vasilevski N.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

Recall that the classical Fock space F2( $$ \mathbb{C} $$ ) is the closed subspace of L2( $$ \mathbb{C} $$ , dμ) consisting of all functions analytic in $$ \mathbb{C} $$ .

Springer Nature

Wiener Algebras

Alpay D., Colombo F., Sabadini I.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

This chapter contains a study of the Wiener algebra to the quaternionic setting in the discrete and continuous case, also including an analogue of the Wiener-Lévy theorem and of the Wiener-Hopf factorization.

Springer Nature

Slice Hyperholomorphic Bergman Spaces

Alpay D., Colombo F., Sabadini I.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

Bergman spaces have been studied in the hypercomplex case, in the context of monogenic functions with values in a Clifford algebra, in particular quaternions. Here we consider Bergman spaces in the slice hyperholomorphic setting. They can be defined in two different ways: one global, one via the complex slices, thus giving the so-called Bergman spaces of the first and of the second kind, respectively.

Springer Nature

de Branges Spaces

Alpay D., Colombo F., Sabadini I.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

In this chapter we extend some results in de Branges’ book (Hilbert Spaces of Entire Functions. Prentice-Hall Inc., Englewood Cliffs, 1968) to the slice hyperholomorphic setting over the quaternions.

Springer Nature

Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces

Alpay D., Colombo F., Sabadini I.

Springer Nature

Operator Theory: Advances and Applications , 2024 , citations by CoLab: 0 | Abstract

The Hilbert spaces studied in this chapter have been considered earlier in the framework of monogenic (or Fueter regular) functions. In this chapter, we shall introduce and study the Bloch, Besov and Dirichlet spaces, in the slice hyperholomorphic case, mainly working on the unit ball $$\mathbb B$$

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