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 |
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