Linear Operators, Part 2 |
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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 ƒ 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 ƒ 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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