2019
Том 71
№ 8

All Issues

Popov G. Ya.

Articles: 6
Article (Russian)

New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics

Popov G. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1642-1652

We construct new integral transformations and present their applications to the construction of exact solutions of some boundary-value problems of mathematical physics. We solve the problem of diffraction of acoustic waves in a circular cone truncated by two spherical surfaces. We also solve the initial boundary-value problem of the theory of heat conduction for the same truncated cone under nonzero initial conditions.

Article (Ukrainian)

On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics

Popov G. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 810-819

We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm–Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and inversion formulas for them. We apply these formulas to the solution of initial boundary-value problems in the theory of heat conduction for circular hollow cones truncated by spherical surfaces.

Article (Ukrainian)

A generalization of Carleman's equation, solved in explicit form, and its application in the theory of bending of plates

Popov G. Ya., Yatsenko Yu. P.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 315–320

Article (Ukrainian)

Dual integral equations associated with Fourier transforms

Nguyen Van Ngok, Popov G. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 188–195

Article (Ukrainian)

A remarkable property of Jacobi polynomials

Popov G. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1968. - 20, № 4. - pp. 540–547

Article (Russian)

On an Integro-Differential Equation

Popov G. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 46-54