On self-adjoint ordinary differential operators.
نویسندگان
چکیده
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 کاملFactorization of self-adjoint ordinary differential equations
Keyword: Factorization method Self-adjoint differential equations Eigenvalue problems This paper deals with the factorization of self-adjoint differential operators Lð2nÞ 1⁄4 1 q d n dx qb d n dx , and their spectral type differential equations. Sufficient conditions of factorization are reported. A large class of differential operators and equations that can be factorized is obtained. The fact...
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 کاملA Characterization of Positive Self-adjoint Extensions and Its Application to Ordinary Differential Operators
A new characterization of the positive self-adjoint extensions of symmetric operators, T0, is presented, which is based on the Friedrichs extension of T0, a direct sum decomposition of domain of the adjoint T ∗ 0 and the boundary mapping of T ∗ 0 . In applying this result to ordinary differential equations, we characterize all positive self-adjoint extensions of symmetric regular differential o...
متن کاملSelf-adjoint commuting differential operators of rank two
This is a survey of results on self-adjoint commuting ordinary differential operators of rank two. In particular, the action of automorphisms of the first Weyl algebra on the set of commuting differential operators with polynomial coefficients is discussed, as well as the problem of constructing algebro-geometric solutions of rank l > 1 of soliton equations. Bibliography: 59 titles.
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: MATHEMATICA SCANDINAVICA
سال: 1956
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10451