Linear Operators: Spectral operators |
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Page 1932
... valued extension property . In this case x ( § ) is a single valued analytic function with domain p ( x ) and with x ( § ) = R ( § ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the ...
... valued extension property . In this case x ( § ) is a single valued analytic function with domain p ( x ) and with x ( § ) = R ( § ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the ...
Page 1990
... valued function f on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is ...
... valued function f on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is ...
Page 2092
... valued extension property . The example of an operator which does not have the single valued extension property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man [ 1 ] gave necessary conditions for an ...
... valued extension property . The example of an operator which does not have the single valued extension property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man [ 1 ] gave necessary conditions for an ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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