Linear Operators, Part 2 |
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Page 2393
... real axis ; moreover , each point in Z is a pole of the resolvent of T and a zero of the function A ( A ) . Since A ... real axis . Consequently , Z is a finite set . Now let λ 。€ Z and let v 。 be the order of λ as a pole of the ...
... real axis ; moreover , each point in Z is a pole of the resolvent of T and a zero of the function A ( A ) . Since A ... real axis . Consequently , Z is a finite set . Now let λ 。€ Z and let v 。 be the order of λ as a pole of the ...
Page 2424
... real numbers , with y > 0 and 1 > B > 0 . Let A ɛ Ay. ̧ ( B ( H ) ) , and let ƒ be an infinitely differentiable H - valued function of a real variable which vanishes outside a bounded interval of the real axis . Then the improper ...
... real numbers , with y > 0 and 1 > B > 0 . Let A ɛ Ay. ̧ ( B ( H ) ) , and let ƒ be an infinitely differentiable H - valued function of a real variable which vanishes outside a bounded interval of the real axis . Then the improper ...
Page 2456
... 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 functions , each vanishing outside a compact subset of the real axis ...
... 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 functions , each vanishing outside a compact subset of the real axis ...
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