A continuation of solutions to convolution equations with the loss of smoothness
Anastasiia Minenkova
TL;DR
This paper investigates how the smoothness of solutions to convolution equations diminishes when extended, providing examples for specific types of convolvers to illustrate the phenomenon.
Contribution
It offers a detailed analysis of smoothness loss in solutions to convolution equations and presents concrete examples for certain convolvers.
Findings
Smoothness of solutions decreases upon continuation.
Examples demonstrate the effect for specific convolvers.
Provides theoretical insights into convolution equation behavior.
Abstract
In the present paper the smoothness loss of a continuation of solutions to convolution equations is studied. Also examples for some kinds of convolvers are given.
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