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 1999
... singular point for the measurable function ƒ defined almost everywhere on if ƒ is not integrable in the sense of Lebesgue on any neighborhood of so . The singular points clearly form a closed set in S which we assume to have measure ...
... singular point for the measurable function ƒ defined almost everywhere on if ƒ is not integrable in the sense of Lebesgue on any neighborhood of so . The singular points clearly form a closed set in S which we assume to have measure ...
Page 2419
... singular rather regular integrals . This circumstance introduces a number of annoying even if non - essential complications into our analysis ; in particular , instead of proceeding directly to the desired application of Theorem 1 , we ...
... singular rather regular integrals . This circumstance introduces a number of annoying even if non - essential complications into our analysis ; in particular , instead of proceeding directly to the desired application of Theorem 1 , we ...
Page 2559
... singular integral operators . Trans . Amer . Math . Soc . 121 , 358–377 ( 1966 ) . 3. On the explicit construction ... singular integral equations , I. Brookhaven Nat . Lab . , Appl . Math . Report 499 , April 1967 . 5. The spectral ...
... singular integral operators . Trans . Amer . Math . Soc . 121 , 358–377 ( 1966 ) . 3. On the explicit construction ... singular integral equations , I. Brookhaven Nat . Lab . , Appl . Math . Report 499 , April 1967 . 5. The spectral ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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