Volchkov V. V.
Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 469-484
We introduce the notion of “$s$”-convolution on the hyperbolic plane $H^2$ and consider its properties. Analogs of the Helgason spherical transform on the spaces of compactly supported distributions in $H^2$ are studied. We prove a Paley –Wiener – Schwartz-type theorem for these transforms.
Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1189-1200
We solve the problem of description of the set of continuous functions in annular subdomains of the n-dimensional sphere with zero integrals over all (n - 1)-dimensional spheres covering the inner spherical cap. As an application, we establish a spherical analog of the Helgason support theorem and new uniqueness theorems for functions with zero spherical means.
Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 272-278
We study functions defined on a sphere with prickled point whose integrals over all admissible “hemispheres” are equal to zero. A condition is established under which the point is a removable set for this class of functions. It is shown that this condition cannot be omitted or noticeably weakened.
Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1332–1347
We study functions on a sphere with zero weighted means over the circles of fixed radius. A description of these functions is obtained in the form of series in special functions.
Ukr. Mat. Zh. - 2013. - 65, № 5. - pp. 611–619
We study generalizations of the class of functions with zero integrals over the balls of fixed radius. An analog of the John uniqueness theorem is obtained for weighted spherical means on a sphere.
Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 435-440
We obtain new integral representations for a hypergeometric function.
Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 417-421
We investigate the accuracy of certain sufficient conditions for multipliers of power series in Hardy spaces.
Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1444–1448
Functions are investigated whose integrals over a given collection of sets are zero. Pompeiu sets are described in terms of the approximation of their indicators by linear combinations of the indicators of balls with special radii.
Ukr. Mat. Zh. - 1991. - 43, № 6. - pp. 723–727