Boundary Value Problems for Operator Differential Equations by Myroslav L. Gorbachuk

, , Comments Off on Boundary Value Problems for Operator Differential Equations by Myroslav L. Gorbachuk

By Myroslav L. Gorbachuk

Show description

Read or Download Boundary Value Problems for Operator Differential Equations PDF

Similar functional analysis books

Analysis III (v. 3)

The 3rd and final quantity of this paintings is dedicated to integration conception and the basics of world research. once more, emphasis is laid on a latest and transparent association, resulting in a good dependent and chic concept and offering the reader with powerful ability for additional improvement. hence, for example, the Bochner-Lebesgue indispensable is taken into account with care, because it constitutes an essential software within the sleek thought of partial differential equations.

An Introduction to Nonlinear Functional Analysis and Elliptic Problems

This self-contained textbook offers the elemental, summary instruments utilized in nonlinear research and their functions to semilinear elliptic boundary worth difficulties. through first outlining the benefits and drawbacks of every process, this entire textual content screens how numerous techniques can simply be utilized to a number of version situations.

Introduction to Functional Analysis

Analyzes the idea of normed linear areas and of linear mappings among such areas, delivering the required starting place for additional examine in lots of components of research. Strives to generate an appreciation for the unifying energy of the summary linear-space standpoint in surveying the issues of linear algebra, classical research, and differential and necessary equations.

Aufbaukurs Funktionalanalysis und Operatortheorie: Distributionen - lokalkonvexe Methoden - Spektraltheorie

In diesem Buch finden Sie eine Einführung in die Funktionalanalysis und Operatortheorie auf dem Niveau eines Master-Studiengangs. Ausgehend von Fragen zu partiellen Differenzialgleichungen und Integralgleichungen untersuchen Sie lineare Gleichungen im Hinblick auf Existenz und Struktur von Lösungen sowie deren Abhängigkeit von Parametern.

Additional info for Boundary Value Problems for Operator Differential Equations

Example text

X) is a polynomial of degree n of the form H. (x) = 2nxn +. The polynomials H. (x) satisfy the following relationship: for m#n 0 J00 e-x2Hn (x) Hm (x) dx = 2n\/-,, n! for m = n. ) form an orthogonal system on e_ , 2. 1) by Hn (x) = 2 2 H,, l `1. = 00 0Hm(n)(x)dx. f-W -oo Form < n, Hr(n) (x) = 0 and thus I = 0. If m = n then 00 I= 2nn! 0o 95 dx = 21-n! oo An m e-" dx = 24n1 c. system is formed by the polynomials H. 4) 2or 4. 5. CHEBYSHEV-LAGUERRE POLYNOMIALS The Chebyshev-Laguerre polynomials are orthogonal on the half-line 0 S x < o with respect to the weight function p (x) = xae-".

X) its expression in terms of 40n: (-1)n J 00 0-(a)Lm(a)(x)dx 0 oo (-1)n0n(n-1)Lm(a)(x) + I (-1)n-1 = (-1)n-1 J 0n(n-1)[Lm(a)(x)]' dx = 0 0 oM S6n(n-1)[Lm(a)(x)], dx. 0 The term which does not involve the integral vanishes because a> -1. Carrying out the integration by parts n times we obtain 1= J0 0. [Lm(a)(x)](n)dx. Form < n, we have [L m(a) (x)] (n) = 0 and therefore 1= 0. When m = n, 1 = a! f cdx = n! f xa+nedx = n! I' (a + n + 1). 0 The orthonormal Chebyshev-Laguerre polynomials are Ln(a)(x) ln(a)(x)= 1.

0 The orthonormal Chebyshev-Laguerre polynomials are Ln(a)(x) ln(a)(x)= 1. ]P (a + n + 1)] 2. 5) REFERENCES V. L. Goncharov, Theory of Interpolation and Approximation of Functions, Gostekhizdat, Moscow, 1954, Chap. 3, 4 (Russian). D. Jackson, Fourier Series and Orthogonal Polynomials, Cams Monograph No. 6, Math. Assoc. , 1941, Chap. 2, 7-10. 36 Preliminary Information A. N. Korkin and E. I. " Collected works of E. I. Zolotarev, Vol. 1, pp. 138-153. I. P. Natanson, Constructive Theory of Functions, Gostekhizdat, Moscow, 1949 (Russian).

Download PDF sample

Rated 4.72 of 5 – based on 47 votes