Linear Operators, Part 2 |
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Page 2066
... continuous map of R3 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 ( f ) = h ( fs + t ) h ( f ) , which shows ...
... continuous map of R3 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 ( f ) = h ( fs + t ) h ( f ) , which shows ...
Page 2443
... continuous in D , and has continuous first and second partial derivatives with respect to x in the interior of D , which can be extended continuously to the whole of D. ДА ( b ) A ( x , x ) = ( x , x ) = 0 , 0 ≤ x ≤1 . дх If A Є 2 ...
... continuous in D , and has continuous first and second partial derivatives with respect to x in the interior of D , which can be extended continuously to the whole of D. ДА ( b ) A ( x , x ) = ( x , x ) = 0 , 0 ≤ x ≤1 . дх If A Є 2 ...
Page 2448
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping q : A → B ( X ) , of norm at most M19 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 q : A → B ( X ) , of norm at most M19 is given ; ( b ) a continuous linear mapping ŋ : A ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
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