On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component

Abstract

For an entirely non-selfadjoint operator with spectrum at zero, the imaginary component of which has an absolutely continuous spectrum (not necessarily dissipative and having lacunas in the spectrum), triangular and functional models are constructed.

New Spline Method for Solving Linear Two-Point Boundary Value Problems

“…By handling equations (25) as the error at collocation points, the expressions are combined using the two-norm formula resulting equation (26). We hope to minimize d 1 (γ) norm as follows:…”

On One Class of Non-Dissipative Operators

“…R e m a r k 1. Conditions (8) are also necessary for the boundedness of the operator B (5). After the partial integration, (8)…”

“…Theorem 2. The function S ∆ (λ) (26) is the monodromy function [5,6], S ∆ (λ) = S(a, λ), of the Cauchy problem…”

“…In [4], the basis property of the system of functions generated by the Dunkl kernels d α (iλ k t) is studied. The functions are given by the formula d(izt) = (1 − zB) −1 I, where B is given by (5) and ϕ(x) = x ν . Consider the general case (not supposing that ϕ(x) has degree dependence).…”

Solving Multispecies Lotka–Volterra Equations by the Daftardar-Gejji and Jafari Method

“…Tese kinds of issues often come up in the actual world when algebra, geometry, and calculus are applied, and they also include continuous variables. Tese issues arise in all areas of study, including the scientifc and social sciences, engineering, health care, and business [1][2][3][4][5][6][7][8][9]. Numerical analysis introduced realistic mathematical models which have become more prevalent in science and engineering over the last 50 years as a result of the expansion in the power and accessibility of digital computers.…”