Kokilashvili, Vakhtang
Published in
Georgian Mathematical Journal

A new scale of weighted grand mixed norm Lebesgue spaces L w 1 p 1 , φ 1 ( L w 2 p 2 , φ 2 ) {L_{w_{1}}^{p_{1},\varphi_{1}}(L_{w_{2}}^{p_{2},\varphi_{2}})} is introduced and the boundedness criteria for multiple singular operators are established.

Kokilashvili, Vakhtang
Published in
Georgian Mathematical Journal

A new scale of weighted grand mixed norm Lebesgue spaces L w 1 p 1 , φ 1 ( L w 2 p 2 , φ 2 ) {L_{w_{1}}^{p_{1},\varphi_{1}}(L_{w_{2}}^{p_{2},\varphi_{2}})} is introduced and the boundedness criteria for multiple singular operators are established.

Kharazishvili, Alexander
Published in
Georgian Mathematical Journal

For certain families of topologies, the existence of a common Sierpiński–Zygmund function (of a common Sierpiński–Zygmund function in the strong sense) is established. In this connection, the notion of a Sierpiński–Zygmund space (of a Sierpiński–Zygmund space in the strong sense) is introduced and examined. The behavior of such spaces under some st...

Kharazishvili, Alexander
Published in
Georgian Mathematical Journal

For certain families of topologies, the existence of a common Sierpiński–Zygmund function (of a common Sierpiński–Zygmund function in the strong sense) is established. In this connection, the notion of a Sierpiński–Zygmund space (of a Sierpiński–Zygmund space in the strong sense) is introduced and examined. The behavior of such spaces under some st...

Sen, Abhijit Silagadze, Zurab K.
Published in
Georgian Mathematical Journal

We prove some trigonometric identities involving Chebyshev polynomials of the second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factor calculations for highly excited states.

Dvalishvili, Phridon Nachaoui, Abdeljalil Tadumadze, Tamaz
Published in
Georgian Mathematical Journal

For the nonlinear functional differential equation with several constant delays, the variation formulas for its solution are proved, in which the effects of perturbations of delays and the initial moment are detected.

Shavadze, Tea
Published in
Georgian Mathematical Journal

For the nonlinear controlled functional differential equations with several constant delays, the local variation formulas of solutions are proved, in which the effects of the discontinuous initial condition and perturbations of delays and the initial moment are detected.

Gürkanlı, Ahmet Turan Sevgen, Yaşar Nuri
Published in
Georgian Mathematical Journal

In this paper we study the boundedness of localization operators associated with the Stockwell transform with symbol in L p {L^{p}} acting on the Wiener amalgam space W ( L p , L q ) ( ℝ ) {W(L^{p},L^{q})(\mathbb{R})} .

Kharazishvili, Alexander
Published in
Georgian Mathematical Journal

It is shown that any function acting from the real line ℝ {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function x → exp ( x 2 ) {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, thi...

Shavadze, Tea
Published in
Georgian Mathematical Journal

For the nonlinear controlled functional differential equations with several constant delays, the local variation formulas of solutions are proved, in which the effects of the discontinuous initial condition and perturbations of delays and the initial moment are detected.