Linear Operators: Spectral operators |
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Page 2029
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Фп Ф T , ( p ) = { __p ( s ) v ( ds ) , RN ΚΕΦ . Similarly , functions on RN may determine ...
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Фп Ф T , ( p ) = { __p ( s ) v ( ds ) , RN ΚΕΦ . Similarly , functions on RN may determine ...
Page 2184
... determined spectral measure . This is the analogue of the general spectral theorem for algebras of normal operators in Hilbert space ( cf. X.2.1 ) . 4 THEOREM . Let 2 be an algebra of operators in the complex B - space X which is the ...
... determined spectral measure . This is the analogue of the general spectral theorem for algebras of normal operators in Hilbert space ( cf. X.2.1 ) . 4 THEOREM . Let 2 be an algebra of operators in the complex B - space X which is the ...
Page 2316
... determined so as to satisfy ko 18h 1 sin Bn = cos ßn . It follows readily that so that It follows that Вп πT = 2 - ( nako ) -1 + 0 ( n - 2 ) , Pn ( t ) = cos ( snt + Sn ) , Sn = ( nπko ) 1 + O ( n − 2 ) . 1 S " ( Pn ( 1 ) ) 2 dt ~ ၂၀ ...
... determined so as to satisfy ko 18h 1 sin Bn = cos ßn . It follows readily that so that It follows that Вп πT = 2 - ( nako ) -1 + 0 ( n - 2 ) , Pn ( t ) = cos ( snt + Sn ) , Sn = ( nπko ) 1 + O ( n − 2 ) . 1 S " ( Pn ( 1 ) ) 2 dt ~ ၂၀ ...
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