Toeplitz operators on Poly-analytic spaces via time-scale analysis

Hutník, Ondrej; Hutníková, Mária

doi:10.7153/oam-08-62

Cited by 14 publications

(6 citation statements)

References 14 publications

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“…A time-frequency approach to TO's acting on (poly)analytic function spaces is described in [3]. A measurable function g : Π → C will be called vertical if there exists a measurable function a : R + → C such that g(w) = a(Im(w)) for almost all w ∈ Π .…”

Section: π)mentioning

confidence: 99%

Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions

Yañez

Hutník

Maximenko

2013

Comptes Rendus. Mathématique

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Section: π)mentioning

confidence: 99%

Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions

Yañez

Hutník

Maximenko

2013

Comptes Rendus. Mathématique

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“…Hutník, Hutníková, Ramírez Ortega, Sánchez-Nungaray, Loaiza, and other authors [18,19,23,26,29] studied vertical and angular Toeplitz operators in polyanalytic and truepolyanalytic spaces, Bergman and Fock. In particular, vertical Toeplitz operators in the n-analytic Bergman space over the upper half-plane are represented in [26] as n×n matrices whose entries are continuous functions on (0, +∞), with some additional properties at 0 and +∞.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Here we give another proof. Write f as in (19). It is known [5, Corollary 1.9] that the derivative ∂ ∂z can be applied to the each term of the series.…”

Section: Bargmann-segal-fock Spaces Of Polyanalytic Functionsmentioning

confidence: 99%

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Maximenko,

Tellería-Romero

2019

Preprint

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The paper considers bounded linear radial operators on the polyanalytic Fock spaces F n and on the true-polyanalytic Fock spaces F (n) . The orthonormal basis of normalized complex Hermite polynomials plays a crucial role in this study; it can be obtained by the orthogonalization of monomials in z and z. First, using this basis, we decompose the von Neumann algebra of radial operators, acting in F n , into the direct sum of some matrix algebras, i.e. radial operators are represented as matrix sequences. Secondly, we prove that the radial operators, acting in F (n) , are diagonal with respect to the basis of the complex Hermite polynomials belonging to F (n) . We also provide direct proofs of the fundamental properties of F n and an explicit description of the C*-algebra generated by Toeplitz operators in F (n) , whose generating symbols are radial, bounded, and have finite limits at infinity.

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“…There are many recent investigations on Toeplitz operators, acting in polyanalytic Bergman spaces over one-dimensional domains [8,15,17,18,24,27]. We hope that this paper can serve as a basis for some multidimensional generalizations, see Remarks 5.10, 5.11, and 6.17.…”

Section: Introductionmentioning

confidence: 86%

Homogeneously polyanalytic kernels on the unit ball and the Siegel domain

Leal-Pacheco,

Maximenko,

Ramos-Vazquez

2021

Preprint

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We prove that the homogeneously polyanalytic functions of total order m, defined by the system of equations Dbe written as polynomials of total degree < m in variables z 1 , . . . , z n , with some analytic coefficients. We establish a weighted mean value property for such functions, using a reproducing property of Jacobi polynomials. After that, we give a general recipe to transform a reproducing kernel by a weighted change of variables.Applying these tools, we compute the reproducing kernel of the Bergman space of homogeneously polyanalytic functions on the unit ball in C n and on the Siegel domain. For the one-dimensional case, analogous results were obtained by Koshelev (1977), Pessoa (2014), Hachadi and Youssfi (2019).

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Toeplitz operators on Poly-analytic spaces via time-scale analysis

Cited by 14 publications

References 14 publications

Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions

Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Homogeneously polyanalytic kernels on the unit ball and the Siegel domain

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