The spaces <InlineEquation ID="IEq4"> <EquationSource Format="TEX">${}^{\alpha ,\beta }\mathcal{A}\mathcal{W}^{a_1,a_2}_{M_{1},M_{2}}, {}^{\alpha ,\beta }\mathcal{B}\mathcal{W}^{a_1,a_2}_{M_{1},M_{2}}, {}^{\alpha ,\beta }\mathcal{C}\mathcal{W}^{a_1,a_2}_{M_{1},M_{2}},$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </mmultiscripts> <mi mathvariant="script">A</mi> <msubsup> <mrow> <mi mathvariant="script">W</mi> </mrow> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>M</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </msubsup> <mo>,</mo> <mmultiscripts> <mrow /> <mrow /> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </mmultiscripts> <mi mathvariant="script">B</mi> <msubsup> <mrow> <mi mathvariant="script">W</mi> </mrow> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>M</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </msubsup> <mo>,</mo> <mmultiscripts> <mrow /> <mrow /> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </mmultiscripts> <mi mathvariant="script">C</mi> <msubsup> <mrow> <mi mathvariant="script">W</mi> </mrow> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>M</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </msubsup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> and their variants are introduced and examined as generalizations of the Gelfand-Shilov spaces of type W. This present study focuses on the characterization of appropriately constructed W-type spaces and explores boundedness properties of the pseudo-differential operators by means of the theory of the coupled fractional Fourier transform. Finally, we acquired the CFrFT of the two-dimensional Morlet wavelet and generated its graphs for various parameter values.

Coupled pseudo-differential operators on $W-$type spaces

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发表日期：

2026年3月5日

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Shraban Das,
Kanailal Mahato

摘要

The spaces ${}^{\alpha ,\beta }\mathcal{A}\mathcal{W}^{a_1,a_2}_{M_{1},M_{2}}, {}^{\alpha ,\beta }\mathcal{B}\mathcal{W}^{a_1,a_2}_{M_{1},M_{2}}, {}^{\alpha ,\beta }\mathcal{C}\mathcal{W}^{a_1,a_2}_{M_{1},M_{2}},$ $^{α, β} A W_{M_{1}, M_{2}}^{a_{1}, a_{2}},^{α, β} B W_{M_{1}, M_{2}}^{a_{1}, a_{2}},^{α, β} C W_{M_{1}, M_{2}}^{a_{1}, a_{2}},$ and their variants are introduced and examined as generalizations of the Gelfand-Shilov spaces of type W. This present study focuses on the characterization of appropriately constructed W-type spaces and explores boundedness properties of the pseudo-differential operators by means of the theory of the coupled fractional Fourier transform. Finally, we acquired the CFrFT of the two-dimensional Morlet wavelet and generated its graphs for various parameter values.

Coupled pseudo-differential operators on \(W-\)type spaces

摘要