Linear Operators: Spectral operators |
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Page 2035
... semi - group for which A is the infinite- simal generator . The semi - group T ( t ) and the function p have the further properties : ( iv ) The derivative q ' ( 0 ) exists and p ' ( 0 ) = Ax ( 0 ) if and only if p ( 0 ) € D ( As ) . ( v ) ...
... semi - group for which A is the infinite- simal generator . The semi - group T ( t ) and the function p have the further properties : ( iv ) The derivative q ' ( 0 ) exists and p ' ( 0 ) = Ax ( 0 ) if and only if p ( 0 ) € D ( As ) . ( v ) ...
Page 2037
... semi - group on [ 0 , ∞ ) of bounded linear operators in HP . Let Ê be the infinitesimal generator of the semi - group ↑ ( t ) , 0 ≤too . It will now be shown that BA . For e D ( B ) , we have , by definition , = lim h → 0 + ↑ ( h ) ...
... semi - group on [ 0 , ∞ ) of bounded linear operators in HP . Let Ê be the infinitesimal generator of the semi - group ↑ ( t ) , 0 ≤too . It will now be shown that BA . For e D ( B ) , we have , by definition , = lim h → 0 + ↑ ( h ) ...
Page 2087
... semi - group S ( t ) , t≥ 0 , of bounded linear operators in Ho and S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for ( in the half plane R ( S ) > 0 . For every ( 0 ) in Ho there is one and only one ...
... semi - group S ( t ) , t≥ 0 , of bounded linear operators in Ho and S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for ( in the half plane R ( S ) > 0 . For every ( 0 ) in Ho there is one and only one ...
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