Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2018; 33(4): 1249-1269

Online first article April 12, 2018      Printed October 31, 2018

https://doi.org/10.4134/CKMS.c170440

Copyright © The Korean Mathematical Society.

Distributional fractional powers of similar operators with applications to the Bessel operators

Sandra M\'onica Molina

Naturales-Universidad Nacional de Mar del Plata

Abstract

This paper provides a method to study the nonnegativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and nonnegative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be nonnegative and we will be able to study its powers. In particular, we have applied this method to Bessel-type operators.

Keywords: fractional Bessel operator, distributional operators, Hankel transform

MSC numbers: Primary 47A60, 26A33, 46F10, 46F12, 46F30