Linear Operators, Part 2 |
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Page 2017
... formal differ- ential operator : ( 15 ) 22 2 781 782 22 Əs 2 22 T Əs 1 G Here we have S1 = RN and S2 is void , so that inequality ( i ) of Theorem 6 is satisfied but equation ( ii ) is not . Thus the natural closed extension Ag of the ...
... formal differ- ential operator : ( 15 ) 22 2 781 782 22 Əs 2 22 T Əs 1 G Here we have S1 = RN and S2 is void , so that inequality ( i ) of Theorem 6 is satisfied but equation ( ii ) is not . Thus the natural closed extension Ag of the ...
Page 2020
... formal differential operator ( 18 ) with A " = 0 has its spectrum o ( A ) the whole complex plane unless A is of ... formal differential operators ( 13 ) , ( 14 ) , and ( 15 ) and the spectra of their natural closed extensions are ...
... formal differential operator ( 18 ) with A " = 0 has its spectrum o ( A ) the whole complex plane unless A is of ... formal differential operators ( 13 ) , ( 14 ) , and ( 15 ) and the spectra of their natural closed extensions are ...
Page 2371
... formal differential operator . The abstract operator - theoretic approach via perturbation theorems used in Section 2 was introduced by J. Schwartz [ 2 ] , and extended by H. P. Kramer [ 2 ] to the general case . Some results similar to ...
... formal differential operator . The abstract operator - theoretic approach via perturbation theorems used in Section 2 was introduced by J. Schwartz [ 2 ] , and extended by H. P. Kramer [ 2 ] to the general case . Some results similar to ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
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