Linear Operators, Part 2 |
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Page 2248
... Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p ... f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a spectral operator ...
... Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p ... f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a spectral operator ...
Page 2456
... F is a continuous function vanishing outside a compact subset of the real axis . Next let F be the characteristic function of an interval of the real axis . Using Theorem XII.2.6 , it follows that we can find a sequence Fr of continuous ...
... F is a continuous function vanishing outside a compact subset of the real axis . Next let F be the characteristic function of an interval of the real axis . Using Theorem XII.2.6 , it follows that we can find a sequence Fr of continuous ...
Page 2488
... Suppose that its derivative f ' is positive , continuous , and of bounded variation , and let V ( ( f ' ) 1 ) be the total variation of the reciprocal of f ' . Prove that eff ( r ) dx 2 max ( f ' ( x ) | -1 ) + V ( ( ƒ ' ) − 1 ) ...
... Suppose that its derivative f ' is positive , continuous , and of bounded variation , and let V ( ( f ' ) 1 ) be the total variation of the reciprocal of f ' . Prove that eff ( r ) dx 2 max ( f ' ( x ) | -1 ) + V ( ( ƒ ' ) − 1 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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