Spectrum and eigenfunctions of the convolution operator on a finite interval with kernel whose transform is a characteristic function

2017 ◽  
Vol 53 (9) ◽  
pp. 1145-1159
Author(s):  
A. A. Polosin
Keyword(s):  
Characteristic Function ◽  
Convolution Operator ◽  
Finite Interval

A new approach to the convolution operator on a finite interval

1996 ◽  
Vol 26 (4) ◽  
pp. 460-475 ◽  
Author(s):  
P. A. Lopes ◽  
A. F. dos Santos
Keyword(s):  
Convolution Operator ◽  
Finite Interval ◽  
New Approach

Adjoint of generalized Cesáro operators on analytic function spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 185-192
Author(s):  
Sunanda Naik ◽  
Pankaj K. Nath
Keyword(s):  
Analytic Function ◽  
Convolution Operator ◽  
Composition Operators ◽  
Mixed Norm ◽  
Averaging Operators ◽  
Mixed Norm Spaces ◽  
Cesaro Averaging ◽  
Analytic Function Spaces ◽  
Appl Math ◽  
Two Parameter

AbstractIn this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint {\mathcal{A}^{b,c}} for {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.

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