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, cilt.50, sa.6, ss.1620-1635, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 6
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15672/hujms.795924
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1620-1635
  • Anahtar Kelimeler: fractional Fourier transform, weighted Lebesgue spaces, compact embedding
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.