Linear Operators: Spectral operators |
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Page 1990
... representation in one of the two forms ( 18 ) or ( 19 ) ( f * q ) ( 8 ) = √ p ( s — t ) f ( t ) dt , RN - ( \ * q ) ( 8 ) = √ ̧ ̧ q ( 8 − t ) λ ( dt ) , RN феб , PEH , determined by a complex valued function f on RN or a complex ...
... representation in one of the two forms ( 18 ) or ( 19 ) ( f * q ) ( 8 ) = √ p ( s — t ) f ( t ) dt , RN - ( \ * q ) ( 8 ) = √ ̧ ̧ q ( 8 − t ) λ ( dt ) , RN феб , PEH , determined by a complex valued function f on RN or a complex ...
Page 2478
... representation theorem , XII.3.16 . By that theorem , H has an ordered representation relative to the self adjoint operator H4 . Let the measure of this ordered representation be μ1 , and let the multiplicity sets be e1 , e2 , ... . By ...
... representation theorem , XII.3.16 . By that theorem , H has an ordered representation relative to the self adjoint operator H4 . Let the measure of this ordered representation be μ1 , and let the multiplicity sets be e1 , e2 , ... . By ...
Page 2520
... representations of bounded non - selfadjoint operators with a real spec- trum . Doklady Akad . Nauk SSSR 126 , 1166–1169 ( 1959 ) . ( Russian ) Math . Rev. 21 # 7438 , 1380 ( 1960 ) . 2. Triangular representation of some operators with ...
... representations of bounded non - selfadjoint operators with a real spec- trum . Doklady Akad . Nauk SSSR 126 , 1166–1169 ( 1959 ) . ( Russian ) Math . Rev. 21 # 7438 , 1380 ( 1960 ) . 2. Triangular representation of some operators with ...
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