Linear Operators, Part 2 |
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Page 2042
... derivatives functions which are the restrictions of the corresponding derivatives of T ,. Thus conclusion ( ii ) of Theorem XIV.4.5 applies with n = N , p = 2 , and k arbitrarily large , to show that all derivatives of T ' , are ...
... derivatives functions which are the restrictions of the corresponding derivatives of T ,. Thus conclusion ( ii ) of Theorem XIV.4.5 applies with n = N , p = 2 , and k arbitrarily large , to show that all derivatives of T ' , are ...
Page 2443
... 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 ; J ( ii ) g ( x , x ) > 0 for 0 ≤ x ≤ 1 , and so g ( x , x ) dx = c . Then , if I ...
... 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 ; J ( ii ) g ( x , x ) > 0 for 0 ≤ x ≤ 1 , and so g ( x , x ) dx = c . Then , if I ...
Page 2447
... derivatives , mapping the interval [ 0 , 1 ] into itself . Let be the inverse of the mapping 4. Let a ( x ) be a complex valued function with two continuous derivatives defined in [ 0 , 1 ] . Put ( f ) ( x ) = exp ( a ( x ) ) f ( ( x ) ...
... derivatives , mapping the interval [ 0 , 1 ] into itself . Let be the inverse of the mapping 4. Let a ( x ) be a complex valued function with two continuous derivatives defined in [ 0 , 1 ] . Put ( f ) ( x ) = exp ( a ( x ) ) f ( ( x ) ...
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