Some compact and non-compact embedding theorems for the function spaces defined by fractional Fourier transform

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Toksoy E., Sandıkçı A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.6, pp.1620-1635, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.15672/hujms.795924
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1620-1635
  • Keywords: fractional Fourier transform, weighted Lebesgue spaces, compact embedding
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The fractional Fourier transform is a generalization of the classical Fourier transform through an angular parameter alpha. This transform uses in quantum optics and quantum wave field reconstruction, also its application provides solving some differrential equations which arise in quantum mechanics. The aim of this work is to discuss compact and non-compact embeddings between the spaces A(alpha,p)(w,omega) (R-d) which are the set of functions in L-w(1)(R-d) whose fractional Fourier transform are in L-omega(p) (R-d). Moreover, some relevant counterexamples are indicated.