Linear Operators, Part 2 |
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Results 1-3 of 22
Page 2257
... evident that , assuming T to be a spectral operator and making use of Corollary 23 , we can use all the steps of this argument in reverse and conclude that , conversely , ( a ) must be satisfied . T - To continue with the main line of ...
... evident that , assuming T to be a spectral operator and making use of Corollary 23 , we can use all the steps of this argument in reverse and conclude that , conversely , ( a ) must be satisfied . T - To continue with the main line of ...
Page 2325
... evident . The roots of sin ( z — a ) -B = 0 are consequently simple and fall into two arithmetic sequences , one of the form z = = 2πn + α + z1 , the other of the form z = 2πn + α + 22 , where 2π > RZ1 ≥ Rz2 ≥ 0 , z1 # 22 . In order ...
... evident . The roots of sin ( z — a ) -B = 0 are consequently simple and fall into two arithmetic sequences , one of the form z = = 2πn + α + z1 , the other of the form z = 2πn + α + 22 , where 2π > RZ1 ≥ Rz2 ≥ 0 , z1 # 22 . In order ...
Page 2327
... evident that a simple zero of M ( μ ( λ ) ) is a simple pole of the resolvent R ( λ ; T ) , so that the first part of the lemma is proved . T - - To prove the second part , let λo be a simple zero of M ( μ ( A ) ) and hence a simple ...
... evident that a simple zero of M ( μ ( λ ) ) is a simple pole of the resolvent R ( λ ; T ) , so that the first part of the lemma is proved . T - - To prove the second part , let λo be a simple zero of M ( μ ( A ) ) and hence a simple ...
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