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 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 ...
Page 2468
... vanishing for i > n and for j > n , and vanishing outside the set [ -n , n ] x [ -n , n ] for all i , j , such that Σ ( 43 ) V ( n ) } = ğ , where 9 : ( a ) = ¶ √ K ( 7 ) ( a , b ) ƒ , ( b ) μ ( db ) , ƒ € H ' . - j = 1 R Let Ф be a ...
... vanishing for i > n and for j > n , and vanishing outside the set [ -n , n ] x [ -n , n ] for all i , j , such that Σ ( 43 ) V ( n ) } = ğ , where 9 : ( a ) = ¶ √ K ( 7 ) ( a , b ) ƒ , ( b ) μ ( db ) , ƒ € H ' . - j = 1 R Let Ф be a ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero