We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara’s extremal weight crystals over the Kac–Moody algebra of type A+∞, and construct a Knuth type correspondence preserving the plactic relations. This bijection yiel...

The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At present time, this has wide applications study non-linear differential equations, linear transport theory, diffraction acoustic electromagnetic waves, scattering inverse scattering, among others. In our work, we use computer algebra system Mathematica implem...

We provide three large classes of control functions that ensure the hyperstability Cauchy equation on restricted domains included in various types commutative semigroups. Among other consequences, we obtain significant improvements similar results known from literature for several Aoki-Rassias-type functions.

In the paper the formulas for derivatives of the Cauchy type integral K[f ] of smooth functions f on the distinguished boundary of a polydisc are given. These formulas express the derivatives of order m from K[f ] through the derivatives of lower order (Theorem 1). We use them for the estimates of smoothness of derivatives of Cauchy type integral in terms of the Holder’s ordinary scale (Theorem...

In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized functions which are intergrable also asymptotic behaviors Cauchy-type integral and Cauchy principal Parabola at infinity. At end, discuss for sectionally holomorphic with as their jump curve obtain explicit form.

The Cauchy–Nicoletti boundary value problem for a system of ordinary differential equations with pole-type singularities is investigated. The conditions of the existence, uniqueness, and nonuniqueness of a solution in the class of continuously differentiable functions are given. The classical Banach contraction principle is combined with a special transformation of the original problem. Introdu...