Pseudo-Differential Operators Associated with the Jacobi Differential Operator
Copyright policy )Pseudo-Differential Operators Associated with the Jacobi Differential Operator
The authors consider pseudo-differential operators on \((0,+\infty)\), defined in terms of the Fourier-Jacobi transform: \[ (Ff)(\xi)=\widehat f(\xi)=\int^\infty_0\varphi_\xi(x)f(x)dm(x) \] where \(\varphi_\xi(x)\) is the Jacobi function and \(dm(x)\) the associated measure. Precisely, for a suitable class of symbols \(p(x,\xi)\), one sets \[ p(x,D)f(x)=F^{-1}_{\xi\to x}\bigl(p(x,\xi)\widehat f(\xi)\bigr). \] The authors study the boundedness of the operators \(p(x,D)\) in different function spaces, giving for them an integral representation.
Jacobi function, Applied Mathematics, Pseudodifferential operators as generalizations of partial differential operators, Pseudodifferential operators, Fourier-Jacobi transform, boundedness, integral representation, Analysis
Jacobi function, Applied Mathematics, Pseudodifferential operators as generalizations of partial differential operators, Pseudodifferential operators, Fourier-Jacobi transform, boundedness, integral representation, Analysis
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