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 2493
... kernels x ( x , y ) and ẞ ( x , y ) . Then BR ( A ) A is the integral operator with the kernel a b ( x , t ) a ( t , y ) dt ; this kernel is Hölder - continuous in all the three parameters λ , x , y . - If we let ( A ) = det2 ( I — BR ...
... kernels x ( x , y ) and ẞ ( x , y ) . Then BR ( A ) A is the integral operator with the kernel a b ( x , t ) a ( t , y ) dt ; this kernel is Hölder - continuous in all the three parameters λ , x , y . - If we let ( A ) = det2 ( I — BR ...
Page 2499
... kernel V ( x , y ) , and in which the Friedrichs similarity method of Section 2 is assumed to apply . Then , as shown in Section 2 , eitH2 ( IT ) -lettH1 ( I + T ) , where is a singular integral operator 2 ( Tƒ ) ( x ) = P | 1 + ∞ 88 G ...
... kernel V ( x , y ) , and in which the Friedrichs similarity method of Section 2 is assumed to apply . Then , as shown in Section 2 , eitH2 ( IT ) -lettH1 ( I + T ) , where is a singular integral operator 2 ( Tƒ ) ( x ) = P | 1 + ∞ 88 G ...
Page 2502
... kernel function & satisfies the integral inequality f | 8 ( λ ) | dồ ≤ || H2 — H1 || 1 , the norm on the right being the trace norm of Chapter XI . Moreover , Krein establishes the trace formula tr ( p ( H2 ) — q ( H1 ) ) = 81 8 ...
... kernel function & satisfies the integral inequality f | 8 ( λ ) | dồ ≤ || H2 — H1 || 1 , the norm on the right being the trace norm of Chapter XI . Moreover , Krein establishes the trace formula tr ( p ( H2 ) — q ( H1 ) ) = 81 8 ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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