Linear Operators, Part 2 |
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Page 1945
... symmetric , and have f ( x , x ) ≥ 0 for all x in H. Let L be given its weak product topology so that , by definition , the sets { ƒ \ ƒ € L , \ f ( x , y ) − g ( x , y ) | < ε } , where x , ye H and ɛ > 0 , form a subbase for the ...
... symmetric , and have f ( x , x ) ≥ 0 for all x in H. Let L be given its weak product topology so that , by definition , the sets { ƒ \ ƒ € L , \ f ( x , y ) − g ( x , y ) | < ε } , where x , ye H and ɛ > 0 , form a subbase for the ...
Page 2307
... symmetric formal differential operator of order n defined on an interval I. Let the deficiency indices of 7 both be equal to an integer m . Let A ,, i = 1 , m , be a set of m linearly independent boundary values for T. Let S be the ...
... symmetric formal differential operator of order n defined on an interval I. Let the deficiency indices of 7 both be equal to an integer m . Let A ,, i = 1 , m , be a set of m linearly independent boundary values for T. Let S be the ...
Page 2308
... symmetric by Lemma XII.4.8 , it follows from Lemma XII.2.1 that f = 0 . This completes the proof of the lemma . Q.E.D. 2 COROLLARY . Let be a formally symmetric formal differential operator defined on a bounded closed interval I. Let S ...
... symmetric by Lemma XII.4.8 , it follows from Lemma XII.2.1 that f = 0 . This completes the proof of the lemma . Q.E.D. 2 COROLLARY . Let be a formally symmetric formal differential operator defined on a bounded closed interval I. Let S ...
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