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 2017
... formal differ- ential operator : ( 15 ) 22 22 2 მ 81 მ 8 , as 22 Əs ? 2 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 A of the ...
... formal differ- ential operator : ( 15 ) 22 22 2 მ 81 მ 8 , as 22 Əs ? 2 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 A of the ...
Page 2020
... formal differential operator ( 18 ) with A1Ø2 = 0 has its spectrum σ ( 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 A1Ø2 = 0 has its spectrum σ ( 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 Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero