Linear Operators, Part 2 |
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Page 1999
... singular point for the measurable function f defined almost everywhere on if f 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 f defined almost everywhere on if f 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 2403
... singular integrals play a role . As compared to the singular integrals treated in the first set of applications , these singular integrals are more seriously divergent . Their treatment . consequently requires the derivation of certain ...
... singular integrals play a role . As compared to the singular integrals treated in the first set of applications , these singular integrals are more seriously divergent . Their treatment . consequently requires the derivation of certain ...
Page 2559
... singular integral operators . Trans . Amer . Math . Soc . 113 , 101-128 ( 1964 ) . 2. Commutators , generalized eigenfunction expansions and singular integral operators . Trans . Amer . Math . Soc . 121 , 358–377 ( 1966 ) . 3 . On the ...
... singular integral operators . Trans . Amer . Math . Soc . 113 , 101-128 ( 1964 ) . 2. Commutators , generalized eigenfunction expansions and singular integral operators . Trans . Amer . Math . Soc . 121 , 358–377 ( 1966 ) . 3 . On the ...
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