Linear Operators: Spectral operators |
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Page 2108
... exists a compact space X , a spectral measure μ on X to A and a bounded Baire measurable function f : XC such that a = Sf ( x ) u ( dx ) . It follows that there exists a spectral measure va defined on a compact subset of C to A such ...
... exists a compact space X , a spectral measure μ on X to A and a bounded Baire measurable function f : XC such that a = Sf ( x ) u ( dx ) . It follows that there exists a spectral measure va defined on a compact subset of C to A such ...
Page 2418
... exists for almost all z " e D. Therefore , by Tonelli's theorem ( III.11.14 ) , the integral ( 75 ) SS141 ( 2 , 2 ) | D | A2 ( z , z ' ) | | zz | f ( z ) dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) ...
... exists for almost all z " e D. Therefore , by Tonelli's theorem ( III.11.14 ) , the integral ( 75 ) SS141 ( 2 , 2 ) | D | A2 ( z , z ' ) | | zz | f ( z ) dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) ...
Page 2441
... exists a finite absolute constant c ' such that I ( α ) ≤ c ' ( 1 + a ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that 4 4 ( 43 ) [ V1 ( r , r ' ) | + | OV ...
... exists a finite absolute constant c ' such that I ( α ) ≤ c ' ( 1 + a ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that 4 4 ( 43 ) [ V1 ( r , r ' ) | + | OV ...
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