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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

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

Erdem Toksoy
Ayşe Sandıkçı
Sayfa
1620–1635
Yayın Tarihi
2022-10-18
DOI
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Moreover, some relevant counterexamples are indicated.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The fractional Fourier transform is a generalization of the classical Fourier transform through an angular parameter $\alpha $.
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Temel Bulgular & Veri:The aim of this work is to discuss compact and non-compact embeddings between the spaces $A_{\alpha ,p}^{w,\omega }\left(\mathbb{R}^{d}\right) $ which are the set of functions in ${L_{w}^{1}\left(\mathbb{R}^{d}\right) }$ whose fractional Fourier transform are in ${L_{\omega}^{p}\left(\mathbb{R}^{d}\right) }$.
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Sonuç & Katkı:Moreover, some relevant counterexamples are indicated.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fractional Fourirer transform · weighted Lebesgue spaces · compact embedding

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 }\left(\mathbb{R}^{d}\right) $ which are the set of functions in ${L_{w}^{1}\left(\mathbb{R}^{d}\right) }$ whose fractional Fourier transform are in ${L_{\omega}^{p}\left(\mathbb{R}^{d}\right) }$. Moreover, some relevant counterexamples are indicated.

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Bu Makaleye Atıf Yap

Toksoy, E., Sandıkçı, A. (2022). Some compact and non-compact embedding theorems for the function spaces defined by fractional Fourier transform. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1620–1635. https://ajindex.com/articles/529512

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Kaynakça (18)

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