Representations of Polynomial Covariance Type Commutation Relations by Linear Integral Operators on $$L_p$$ Over Measure Spaces

Abstract

AbstractRepresentations of polynomial covariance type commutation relations by linear integral operators on \(L_p\) over measures spaces are constructed. Conditions for such representations are described in terms of kernels of the corresponding integral operators. Representation by integral operators are studied both for general polynomial covariance commutation relations and for important classes of polynomial covariance commutation relations associated to arbitrary monomials and to affine functions. Examples of integral operators on \(L_p\) spaces representing the covariance commutation relations are constructed. Representations of commutation relations by integral operators with special classes of kernels such as separable kernels and convolution kernels are investigated.KeywordsIntegral operatorsCovariance commutation relationsConvolutionMSC 202047G1047L8081D0547L65