Classification of self-adjoint domains of odd-order differential operators with matrix theory
نویسندگان
چکیده
Abstract In this article, we investigate the classification of self-adjoint boundary conditions odd-order differential operators. We obtain that for under some assumptions, there are exactly two basic types conditions: coupled and mixed. Moreover determine number possible each type, which is different from even-order cases. Our construction will play an important role in canonical forms spectral analysis these
منابع مشابه
Non-self-adjoint Differential Operators
We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...
متن کاملOscillation Results for Second Order Self-adjoint Matrix Differential Systems
on [0,∞), where Y (t), P (t) and Q(t) are n × n real continuous matrix functions on [0,∞) with P (t), Q(t) symmetric and P (t) positive definite for t ∈ [0,∞) (P (t) > 0, t ≥ 0). A solution Y (t) of (1.1) is said to be nontrivial if det Y (t) 6= 0 for at least one t ∈ [0,∞) and a nontrivial solution Y (t) of (1.1) is said to be prepared (selfconjugated) if Y ∗(t)P (t)Y ′(t)− Y ∗′(t)P (t)Y (t) ≡...
متن کاملAdjoint and self - adjoint differential operators on graphs ∗
A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...
متن کاملHALF-EIGENVALUES OF SELF-ADJOINT, 2mTH ORDER DIFFERENTIAL OPERATORS AND SEMILINEAR PROBLEMS WITH JUMPING NONLINEARITIES
We consider semilinear boundary value problems of the form Lu(x) = f(x, u(x)) + h(x), x ∈ (0, π), (1) where L is a 2mth order, self-adjoint, disconjugate ordinary differential operator on [0, π], together with appropriate boundary conditions at 0 and π, while f : [0, π] × R → R is a Carathéodory function and h ∈ L2(0, π). We assume that the limits a(x) := lim ξ→∞ f(x, ξ)/ξ, b(x) := lim ξ→−∞ f(x...
متن کاملSpectral Theory for Compact Self-Adjoint Operators
This agrees with the definition of the spectrum in the matrix case, where the resolvent set comprises all complex numbers that are not eigenvalues. In terms of its spectrum, we will see that a compact operator behaves like a matrix, in the sense that its spectrum is the union of all of its eigenvalues and 0. We begin with the eigenspaces of a compact operator. We start with two lemmas that we w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Open Mathematics
سال: 2023
ISSN: ['2391-5455']
DOI: https://doi.org/10.1515/math-2023-0104