An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

2016 ◽  
Vol 94 (3) ◽  
pp. 618-631 ◽  
Author(s):  
Constantin Buşe ◽  
Donal O’Regan ◽  
Olivia Saierli
Keyword(s):  
Convolution Operator ◽  
Evolution Family ◽  
Growth Bound

scholarly journals A New Estimation of the Growth Bound of a Periodic Evolution Family on Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Constantin Buse ◽  
Aftab Khan ◽  
Gul Rahmat ◽  
Afshan Tabassum
Keyword(s):  
Banach Spaces ◽  
Evolution Family ◽  
Growth Bound

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}.

scholarly journals A Uniqueness Result for a Simple Superlinear Eigenvalue Problem

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Simulations ◽  
Convolution Operator ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Constitutive Laws ◽  
Parameter Family ◽  
Shape Constraint ◽  
Special Case ◽  
Nonlinear Eigenfunctions

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.

scholarly journals Graph matching as a graph convolution operator for graph neural networks

2021 ◽  
Author(s):  
Maxime Martineau ◽  
Romain Raveaux ◽  
Donatello Conte ◽  
Gilles Venturini
Keyword(s):  
Neural Networks ◽  
Convolution Operator ◽  
Graph Matching ◽  
Graph Neural Networks

scholarly journals A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Convolution Operator ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Open Unit Disc ◽  
Coefficient Inequalities ◽  
Uniformly Starlike Functions ◽  
Convex And Starlike Functions ◽  
Uniformly Starlike

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.

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