In this chapter we study the spectrum of a compact operator. The spectrum of these operators is much simpler to describe than that of an arbitrary continuous linear operator. In a later chapter we will give applications to Sturm-Liouville differential operators.#LetX 6 ≠ {0}be a complex ...
Most of the spectral properties of a compact operator in a Banach space were discovered by F. Riesz, and appeared in a paper in 1918 (several years before Banach's book). These results were augmented and simplified by the work of Schauder. What follows is an exposition of these ideas....
The spectrum of the product of operators, and the product of their numerical ranges We show that a compact operator A is a multiple of Wong,Ngai-Ching,Wang,... - 《Linear Algebra & Its Applications》 被引量: 5发表: 2015年 Spectrum of the direct sum of operators We study the connection...
, and that 𝑇 is AMD-regular if and only if the essential spectrum of |𝑇| consists of a single point. Key words and phrases::AMD-numbers;compact operator;strictly singular operator;superstrictly singular operator;Calkin algebra;essential spectrum...
Approximation of the spectrum of a non-compact operator given by the magnetohydrodynamic stability of a plasma The study of the magnetohydrodynamic stability of a plasma leads to a problem of determination of the spectrum of a non-compact selfadjoint operator A . Th... J Rappaz - 《Numerische...
On the negative discrete spectrum of the operator-N-aV for a class of unbounded domains in R 来自 ResearchGate 喜欢 0 阅读量: 14 作者: M. Solomyak 摘要: Presents an excerpt from the book "Passage to a Human World: How an Edifice of Error Blocks Our View of What Is Happening in ...
THE ALGEBRA OF SMOOTH FUNCTIONS OF RAPID DESCENT A bounded operator with the spectrum lying in a compact set V R, has C ∞ (V) functional calculus. On the other hand, an operator H acting on a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So in a Banac...
In this paper the author studies the following related problem: how many eigenvalues of the Laplace operator it takes to determine the dimension? The following answer is obtained: If M is a connected compact Riemannian manifold without boundary such that the sectional curvature is bounded from ...
Denote by σ(A), σ pp (A), σ ac (A) and σ sing (A) the spectrum, point spectrum, absolutely continuous spectrum and singular spectrum of a selfadjoint operator A, respectively. Theorem 1. Assume that the distribution of V n (ω) admits the bounded density with a compact support....
We compare the low-lying spectrum of the staggered Dirac operator in the\nconfining phase of compact U(1) gauge theory on the lattice to predictions of\nchiral random matrix theory. The small eigenvalues contribute to the chiral\ncondens... BA Berg,H Markum,R Pullirsch,... - The American...