Linear Operators: Spectral operators |
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Page 2010
... vanishes on Used , σ ( Â ( s ) ) , and since q is continuous , it also vanishes on the closure of this set . Thus Corollary 9.9 shows that o vanishes on σ ( A ) , which means that 9 = 0 . Ф To prove ( 76 ) it is seen from Theorem 9.3 ...
... vanishes on Used , σ ( Â ( s ) ) , and since q is continuous , it also vanishes on the closure of this set . Thus Corollary 9.9 shows that o vanishes on σ ( A ) , which means that 9 = 0 . Ф To prove ( 76 ) it is seen from Theorem 9.3 ...
Page 2064
... vanishes identically and 0 = fo = f . α = Q.E.D. This theorem shows that if the function ( 3 ) vanishes on 1 then = â ( ∞0 ) = 0 , ƒ ( 8 ) = 0 , and ƒ = 0 . Hence the operator a in A1 given by equation ( 2 ) determines a and ƒ uniquely ...
... vanishes identically and 0 = fo = f . α = Q.E.D. This theorem shows that if the function ( 3 ) vanishes on 1 then = â ( ∞0 ) = 0 , ƒ ( 8 ) = 0 , and ƒ = 0 . Hence the operator a in A1 given by equation ( 2 ) determines a and ƒ uniquely ...
Page 2261
... vanishes if à is in the resolvent set , we may also write ( 3 ) y * ƒ ( T ) yo = 1 2mi Sam f ( X ) { R * ( \ , y * , yo ) — R− ( λ , yo , yo ) } dλ , Σπί σ ( T ) for f vanishing at least to second order at - Yo Yo , yo € * O and at ...
... vanishes if à is in the resolvent set , we may also write ( 3 ) y * ƒ ( T ) yo = 1 2mi Sam f ( X ) { R * ( \ , y * , yo ) — R− ( λ , yo , yo ) } dλ , Σπί σ ( T ) for f vanishing at least to second order at - Yo Yo , yo € * O and at ...
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