A Generalized (λ, µ)- Slant Hankel Operators on the Lebesgue Space L^2(T)

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Published: 2024-12-15
Keywords:
Toeplitz operator, Hankel operator, Slant Hankel operator, Lebesgue space, Hardy space, λ - Hankel operator, λ - Slant Hankel operator

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Shesh Kumar Pandey
Department of Mathematics, A.N.D.K.P.G. College, Babhnan, Gonda, U.P., India
Anand Prakash Mishra
Department of Mathematics, A.N.D.K.P.G. College, Babhnan, Gonda, U.P., India

Abstract

In this paper, we shall look for the solution of an operator equation µMz*X-XMzk = λX, for k ≥1 and λ, µ in ℂ. Its solutions will provide a class of operators, which can be considered as generalization of λ– Hankel operator (introduced by Avendano). We also analyze certain elementary properties of generalized (λ, µ) - slant Hankel operator on the Lebesgue space of unit circle T. We also discuss an analogous result to the famous Kronecker theorem of Hankel matrix for generalized (λ, µ) - slant Hankel operator.

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Vol. 28 No. 4 (2024): Table of Content

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A Generalized (λ, µ)- Slant Hankel Operators on the Lebesgue Space L^2(T). J. Int. Acad. Phys. Sci. [Internet]. 2024 Dec. 15 [cited 2026 Oct. 23];28(4):339-54. Available from: http://www.iaps.org.in/journal/index.php/journaliaps/article/view/1024

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