Toeplitz Operators with Vertical Symbols Acting on the Poly-Bergman Spaces of the Upper Half-Plane

Ortega, Josué Ramírez; Sánchez-Nungaray, Armando

doi:10.1007/s11785-015-0469-4

Cited by 19 publications

(14 citation statements)

References 7 publications

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“…Comparing our Theorem 1.1 with the main results of [23,26,29], we would like to point out three differences.…”

Section: Introduction and Main Resultsmentioning

confidence: 92%

“…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%

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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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“…Comparing our Theorem 1.1 with the main results of [23,26,29], we would like to point out three differences.…”

Section: Introduction and Main Resultsmentioning

confidence: 92%

Section: Introduction and Main Resultsmentioning

confidence: 99%

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Maximenko,

Tellería-Romero

2019

Preprint

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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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“…In [5], J. Ramírez-Ortega and A. Sánchez-Nungaray described the * -algebra generated by the Toeplitz operators with bounded vertical symbols and acting over each poly-Bergman space in the upper plane A 2 (Π). They considered bounded vertical symbols that have limit values at = 0, ∞ and prove that the * -algebra generated by the Toeplitz operator acting on A 2 (Π) with this kind of symbols is isomorphic and isometric to the * -algebra of matrix-valued functions of the compact [0, ∞].…”

Section: (C −| |mentioning

confidence: 99%

Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces

Sánchez-Nungaray

Gonzalez-Flores

López-Martínez

et al. 2018

Journal of Function Spaces

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We describe the C⁎-algebra generated by the Toeplitz operators acting on each poly-Fock space of the complex plane C with the Gaussian measure, where the symbols are bounded functions depending only on x=Re z and have limit values at y=-∞ and y=∞. The C⁎ algebra generated with this kind of symbols is isomorphic to the C⁎-algebra functions on extended reals with values on the matrices of dimension n×n, and the limits at y=-∞ and y=∞ are scalar multiples of the identity matrix.

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Toeplitz Operators with Vertical Symbols Acting on the Poly-Bergman Spaces of the Upper Half-Plane

Cited by 19 publications

References 7 publications

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Homogeneously polyanalytic kernels on the unit ball and the Siegel domain

Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces

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