Linear Operators: Spectral operators |
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Page 2068
... satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo LOL satisfies ( 11 ) . More generally ...
... satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo LOL satisfies ( 11 ) . More generally ...
Page 2112
... satisfies the condition : ( α ) N ( F1 , T ) ≤ M ( F2 , T ) , 1 if F1 the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X ...
... satisfies the condition : ( α ) N ( F1 , T ) ≤ M ( F2 , T ) , 1 if F1 the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X ...
Page 2385
... satisfies ( 23 ) fu also satisfies fu = Kufu + 1 , −ƒ “ ( t ) + 2iμfű ( t ) + q ( t ) fu ( t ) = 0 , and thus the function ( 24 ) Ju ( t ) = e - tutf ( t ) - μ will satisfy the differential equation 79729. By ( 9 ) and Lemma VII.6.1 ...
... satisfies ( 23 ) fu also satisfies fu = Kufu + 1 , −ƒ “ ( t ) + 2iμfű ( t ) + q ( t ) fu ( t ) = 0 , and thus the function ( 24 ) Ju ( t ) = e - tutf ( t ) - μ will satisfy the differential equation 79729. By ( 9 ) and Lemma VII.6.1 ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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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