Linear Operators: Spectral operators |
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Page 2066
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
Page 2443
... continuous partial derivatives of all orders up to the second everywhere in the interior of D , and that these derivatives may be extended continuously to the whole of D ; > 0 ( ii ) g ( x , x ) > 0 for 0 ≤ x ≤ 1 , and S. g ( x , x ) ...
... continuous partial derivatives of all orders up to the second everywhere in the interior of D , and that these derivatives may be extended continuously to the whole of D ; > 0 ( ii ) g ( x , x ) > 0 for 0 ≤ x ≤ 1 , and S. g ( x , x ) ...
Page 2448
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping 9 : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping 9 : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero