L -invariant and radial singular integral operators on the Fock space

Dogga, Venku Naidu (2023) L -invariant and radial singular integral operators on the Fock space. Journal of Pseudo-Differential Operators and Applications, 14 (1). p. 11. ISSN 1662-9981

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Abstract

For a unitary matrix X of order n over the field of complex numbers and an entire function φ belonging to the Fock space F2: = F2(Cn) , we define an integral operator on F2(Cn) of the form (HφXf)(z)=∫Cnf(w)φ(z+X∗Xw¯)ezw¯dλ(w).Here dλ(z)=π-ne-|z|2dz is a Gaussian measure on Cn. We characterize all the symbols φ for which the operator HφX is bounded. Next, we consider integral operator on F2 defined by (Rφf)(z)=∫Cnf(w)φ(z⋆w¯)dλ(w)for φ∈ F2, where ⋆ is a coordinatewise multiplication. We give a complete characterization for the symbols φ∈ F2(Cn) so that the operator Rφ is bounded on F2. In addition to boundedness, we also obtain some fundamental results for the operators HφX and Rφ such as normality, the C∗-algebra properties, the spectrum and the compactness. Moreover, we characterize the common reducing subspaces for each of the collections BX={HφX∈B(F2):φ∈F2},R={Rφ∈B(F2):φ∈F2},respectively.

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IITH Creators:

IITH Creators	ORCiD
Dogga, Venku Naidu	http://www.orcid.org/0000-0002-1279-0105

Item Type:

Article

Uncontrolled Keywords:

Bargmann transform; Fock space; Fourier transform; L-invariant operator; Multiplication operator; Radial operator; Reducing subspace; Singular integral operator; Gaussian; Fock space

Subjects:

Mathematics
Mathematics > Probabilities and applied mathematics

Divisions:

Department of Mathematics

Depositing User:

Mr Nigam Prasad Bisoyi

Date Deposited:

22 Aug 2023 05:40

Last Modified:

22 Aug 2023 05:40

URI:

http://raiithold.iith.ac.in/id/eprint/11601