Linear Operators: Spectral operators |
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Page 2300
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E , ) = 0 if μ is ...
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E , ) = 0 if μ is ...
Page 2333
... finite . that Since f is in L2 ( 0 , ∞ ) , it is sufficient by Schwarz's inequality to show 00 f ( s ) s + t ds | g ( t ) = √ ; = f ( ut ) du 0 1 + u belongs to L2 ( 0 , ∞ ) . Putting f ( x ) = f ( tx ) , we may use Theorem III.11.17 ...
... finite . that Since f is in L2 ( 0 , ∞ ) , it is sufficient by Schwarz's inequality to show 00 f ( s ) s + t ds | g ( t ) = √ ; = f ( ut ) du 0 1 + u belongs to L2 ( 0 , ∞ ) . Putting f ( x ) = f ( tx ) , we may use Theorem III.11.17 ...
Page 2441
... 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 / s ( r , r ...
... 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 / s ( r , r ...
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