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 2130
... coefficients , while spectral theoretic notions are simpler for complex coefficients . To bridge this gap , we employ the following construction . If X is a real B - space which is ordered by ≤ , let 1 = X → X and define : ( a + iẞ ) ...
... coefficients , while spectral theoretic notions are simpler for complex coefficients . To bridge this gap , we employ the following construction . If X is a real B - space which is ordered by ≤ , let 1 = X → X and define : ( a + iẞ ) ...
Page 2323
... coefficients in the boundary conditions , that is , on the coefficients aim and Bt.mi of the highest derivative occurring with a non - zero coefficient . At any rate , if Regularity Hypothesis 1 is satisfied , it follows from ( 11 ) ...
... coefficients in the boundary conditions , that is , on the coefficients aim and Bt.mi of the highest derivative occurring with a non - zero coefficient . At any rate , if Regularity Hypothesis 1 is satisfied , it follows from ( 11 ) ...
Page 2338
... coefficients a and b are identical up to a common factor of modulus 1 with the coefficients ã , and b , of equation ( 48 ) . Thus , for a normalized set of boundary conditions , Hypotheses 9 and 10 depend only on the “ leading " ...
... coefficients a and b are identical up to a common factor of modulus 1 with the coefficients ã , and b , of equation ( 48 ) . Thus , for a normalized set of boundary conditions , Hypotheses 9 and 10 depend only on the “ leading " ...
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