On the convolution equations over the quarter-plane.
On the convolution in the space
On the determination of the Plancherel measure for Lebedev-Whittaker transforms on GL(n)
On the distributional Stieltjes transformation.
On the dual of weighted of the half-space
On the Eigenproblem for Convolution Integral Equations.
On the equivalence of Widder-Miyadera's and Leviatan's representability conditions for the Laplace transform of integrable vector-valued functions
On the expected value of vector lattice-valued random variables
On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms
We deal with several classes of integral transformations of the form where is an operator. In case is the identity operator, we obtain several operator properties on with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on and define the inversion formula. Further, for an other class of differential operators of finite...
On the Fourier transform, Boehmians, and distributions
We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.
On the generalization of the Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
On the Generalized Associated Legendre Functions
Mathematics Subject Classification: 33C60, 33C20, 44A15This paper is devoted to an important case of Wright’s hypergeometric function 2Fτ,β1(a, b; c; z) = 2Fτ,β1(z), to studying its basic properties and to application of 2Fτ,β1(z) to the generalization of the associated Legendre functions.
On the Haagerup inequality and groups acting on -buildings
Let be a group endowed with a length function , and let be a linear subspace of . We say that satisfies the Haagerup inequality if there exists constants such that, for any , the convolutor norm of on is dominated by times the norm of . We show that, for , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on . If is a word length function on a finitely generated group , we show that,...
On the hessian of the optimal transport potential
We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli. We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised Reverse...
On the homogeneous difference equation in the field of Mikusiński operators.
On the image of a generalized -plane transform on .
On the integrability of a class of integral transforms
On the integrability of the ergodic Hilbert transform for a class of functions with equal absolute values.
On the integral transformation associated with the product of gamma-functions.
On the integration schemes of retrieving impulse response functions from transfer functions.