Linear Operators: Spectral operators |
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Page 2017
... formal differ- ential operator : ( 15 ) 22 2 i 781 782 a2 as 2 1 22 Əs2 0 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 2 i 781 782 a2 as 2 1 22 Əs2 0 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 2305
... formal differential operator d dt d 2x2 282 + ( 1-12 ) + dt 1 + t 1 t of the first part of Section XIII.8 , and again make the assumption made there that a , B. Then by the theory of Chapter XIII ( compare the discussion in Section XIII ...
... formal differential operator d dt d 2x2 282 + ( 1-12 ) + dt 1 + t 1 t of the first part of Section XIII.8 , and again make the assumption made there that a , B. Then by the theory of Chapter XIII ( compare the discussion in Section XIII ...
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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 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