Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
From inside the book
Results 1-3 of 77
Page 1976
... integral ( ii ) ↓ ç ( \ ) E ( dλ ; Â ( s ) ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) S_E ( σ ; Â ( s ) ) e ( ds ) , σε β , G is a bounded , countably additive spectral measure in HP and ( iv ) ...
... integral ( ii ) ↓ ç ( \ ) E ( dλ ; Â ( s ) ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) S_E ( σ ; Â ( s ) ) e ( ds ) , σε β , G is a bounded , countably additive spectral measure in HP and ( iv ) ...
Page 1990
... integral , that is , whether the integral is an ordinary Lebesgue integral defined for almost all s , a Cauchy type principal value integral defined as a certain limit of Lebesgue integrals , an integral of a vector valued function , or ...
... integral , that is , whether the integral is an ordinary Lebesgue integral defined for almost all s , a Cauchy type principal value integral defined as a certain limit of Lebesgue integrals , an integral of a vector valued function , or ...
Page 2405
... integral ( 14 ) ( Ah ) ( s ) = f | A ( s , t ) | h ( t ) μ ( dt ) S exists for μ - almost all s , and that , writing | ƒ , for the norm of an element f of L. ( S , Σ , μ ) , we have | Ãh ] , ≤ { A } , | h | ,. Thus , using Theorem III ...
... integral ( 14 ) ( Ah ) ( s ) = f | A ( s , t ) | h ( t ) μ ( dt ) S exists for μ - almost all s , and that , writing | ƒ , for the norm of an element f of L. ( S , Σ , μ ) , we have | Ãh ] , ≤ { A } , | h | ,. Thus , using Theorem III ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
23 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero