Niyaz Tokmagambetov

Pseudo-differential operators generated by a non-local boundary value problem

Pseudo-differential operators and -toroidal symbols generated by a non-local boundary value problem are investigated. A formula for compositions with pseudo-differential operators generated by a non-local boundary value problem is derived. In the Hilbert space concepts of the Fourier transform and convolution generated by a non-local boundary value problem are introduced.

Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field

In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a ‘very weak solution’ adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional-type solutions under conditions when such solutions also exist.

Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed

Given a Hilbert space

Convolution, Fourier analysis, and distributions generated by Riesz bases

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The Green function and correctly solvable non–local boundary value problems for the polyharmonic equation in a punctured domain

H, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting on

A uniqueness theorem of a boundary inverse problem of a differential operator on an interval with integro-differential boundary conditions

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