Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 88
Page 2264
... spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v。I ) E2 ( { vo } ) = 0 , E2 ( · ) being the spectral ...
... spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v。I ) E2 ( { vo } ) = 0 , E2 ( · ) being the spectral ...
Page 2507
... spectrum of H , while the integrals and + ∞0 [ * | A4 ( ( λ ± iɛ ) I — H1 ) − 1v | 2 dλ -∞ + ∞ [ * ~ | B ... spectrum of H can change drastically . In particular , the " absolutely continuous spectrum " o ( Hac ( h ) ) ( cf ...
... spectrum of H , while the integrals and + ∞0 [ * | A4 ( ( λ ± iɛ ) I — H1 ) − 1v | 2 dλ -∞ + ∞ [ * ~ | B ... spectrum of H can change drastically . In particular , the " absolutely continuous spectrum " o ( Hac ( h ) ) ( cf ...
Page 2591
... Spectrum , of a spectral operator , XV.8 ( 1954 ) condition to be in point spectrum , XV.15.13 ( 2076 ) continuous spectrum , definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point spectrum ...
... Spectrum , of a spectral operator , XV.8 ( 1954 ) condition to be in point spectrum , XV.15.13 ( 2076 ) continuous spectrum , definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point spectrum ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero