Algebraic and differential properties of polynomial Fourier transformation
The main result of the paper formulated in Theorem~6 deals with the generalized polynomial Fourier transformation. Namely, the convolution theorem is proved for the case of the polynomial Fourier transformation. Moreover, classical results related to differentiation of generalized (in the Sobolev-Schwartz sense) functions are extended to the case of the generalized polynomial Fourier transformation. Finally, Theorem~7 demonstrates that the generalized polynomial Fourier transformation acts as a homomorphism of appropriate algebras.
polynomials on infinite-dimensional spaces
scientific article; zbMATH DE number 7192746
scientific article