Related papers: Extension of Krein's special method for solving in…
A detailed discussion of the Krein's results (applicable for solving the inverse scattering problem) is given with complete proofs.
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
The universal method of expansion of integrals is suggested. It allows in particular to derive the threshold expansion of Feynman integrals.
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions. Applications to solvable quantum-mechanical problems are discussed.
In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are…
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving…
We extend two theorems of Krein concerning entire functions of Cartwright class, and give applications for the Bernstein weighted approximation problem.
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
In this work we extend the range of applicability of a method recently introduced where coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. Some general consequences of the present…
The paper reports on a recent construction of M-functions and Krein resolvent formulas for general closed extensions of an adjoint pair, and their implementation to boundary value problems for second-order strongly elliptic operators on…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.
To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other methods which are based on integrable scalar nonlinear partial…
By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before…