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 |
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Page 2300
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , IE , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I — E „ ) = 0 if μ is not ...
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , IE , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I — E „ ) = 0 if μ is not ...
Page 2333
... finite . 0 f ( t ) f ( s ) t + s dt ds Since ƒ is in L2 ( 0 , co ) , it is sufficient by Schwarz's inequality to show that g ( t ) = √ 00 f ( s ) 8 + t 00 ds S f ( ut ) du 1+ u belongs to L2 ( 0 , ∞ ) . Putting f ( x ) = f ( tx ) , we ...
... finite . 0 f ( t ) f ( s ) t + s dt ds Since ƒ is in L2 ( 0 , co ) , it is sufficient by Schwarz's inequality to show that g ( t ) = √ 00 f ( s ) 8 + t 00 ds S f ( ut ) du 1+ u belongs to L2 ( 0 , ∞ ) . Putting f ( x ) = f ( tx ) , we ...
Page 2441
... finite absolute constant c ' such that I ( a ) | ≤ c ' ( 1 + | a | ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that ε ( 43 ) | V1 ( r , r ' ) | + av 4 др av1 ...
... finite absolute constant c ' such that I ( a ) | ≤ c ' ( 1 + | a | ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that ε ( 43 ) | V1 ( r , r ' ) | + av 4 др av1 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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