Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
On the integral transformation associated with the product of gamma-functions.
On the Lebedev transformation in Hardy's spaces.
On the Mehler-Fock integral transform in L-spaces.
On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.
We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operator Ax = x2 - x d/dx [x d/dx], and its k-th iterates Ak x, where k = 0, 1, ... , and A0 xφ = φ. Comparing with other testing-function spaces,...
Integral transforms of the Kontorovich-Lebedev convolution type.
The generalizations of integral analog of the Leibniz rule on the G-convolutions.
An integral analog of the Leibniz rule for the operators of fractional calculus was considered in paper [1]. These operators are known to belong to the class of convolution transforms [2]. It seems very natural to try to obtain some new integral analog of the Leibniz rule for other convolution operators. We have found a general method for constructing such integral analogs on the base of notion of G-convolution [4]. Several results obtained by this method are represented in this article.
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