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Domingos Djinja

Publications and source records attributed to Domingos Djinja.

6 recordsLinked to original sources
arXiv2023

Differential and linear integral operators representing polynomial covariance commutation relations in $C^\infty$

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance commutation relations by pairs consisting of a differential and linear integral operator are considered including conditions on kernels and coefficients of operators, and examples.

math.FA↗
arXiv2023

Volterra integral operators and general linear integral operators representing polynomial covariance type commutation relations on $L_p$ spaces

Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining 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. Representations of the covariance type commutation relations by integral Volterra operators and integral convolution operators are investigated.

math.FA↗
arXiv2023

Convergence of commutator of linear integral operators with separable kernel representing monomial covariance type commutation relations in $L_p$

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations extending simultaneously the covariance and the reciprocal covariance type commutation relations. Necessary and sufficient conditions for the defining kernels of the integral operators are obtained for the operators to satisfy such commutation relations associated to pairs of polynomials. Representations by integral operators are studied both for general polynomial covariance type commutation relations and for important classes of polynomial covariance commutation relations associated with arbitrary monomials and affine functions. The convergence of commutators of operators in the sequences of non-commuting operators satisfying the corresponding monomial covariance commutation relation is investigated, and the sequences of such non-commuting operators converging to commuting operators, are presented.

math.FA↗
arXiv2023

Representations of polynomial covariance type commutation relations by linear integral operators with separable kernels in $L_p$

Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance type commutation relations are obtained in terms of their kernels. For important classes of polynomial covariance commutation relations associated to arbitrary monomials and to affine functions, these conditions on the kernels are specified in terms of the coefficients of the monomials and affine functions. By applying these conditions, examples of integral operators on $L_p$ spaces, with separable kernels representing covariance commutation relations associated to monomials, are constructed for the kernels involving multi-parameter trigonometric functions, polynomials, and Laurent polynomials on bounded intervals. Commutators of these operators are computed and exact conditions for commutativity of these operators in terms of the parameters are obtained.

math.FA↗