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We introduce the Fresnel type class ℱA1,A2a,b. We also establish the existence of the generalized analytic Fourier-Feynman transform for functionals in the Banach algebra ℱA1,A2a,b

journal of function spaces and applications/journal of function spaces and applications

Generalized Analytic Fourier-Feynman Transform of Functionals in a Banach Algebra<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msubsup><mml:mi>ℱ</mml:mi><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>

Generalized Analytic Fourier-Feynman Transform of Functionals in a Banach AlgebraℱA1,A2a,b