Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In case a noncompact group, term “Fourier sums” should understood as “partial Fourier integrals”. A certain weighted version result is also provided. This leads...

In this paper we consider integrals of the form / e-xK(x,y)f(x)dx, Jo with / 6 C[0, oo) n C«(0, oo), q > p > 0, and x¡f^'\x) 6 C[0, oo), / = I, ... , q -p , when q > p . They appear for instance in certain WienerHopf integral equations and are of interest if one wants to solve these by a Nyström method. To discretize the integral above, we propose to use a product rule of interpolatory type bas...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

Several problems of mathematical physics lead to Fredholm integral equations of the second kind where the kernels are either weakly or strongly singular and the known terms are smooth. These equations have solutions which are smooth in the whole interval of integration except at the endpoints where they have mild singularities. In this paper we derive new pointwise and uniform polynomial approx...