Linear Operators, Part 2 |
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Page 1926
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined by the equations Ν - Τ- Σ λε ( λ ) , λεσ ...
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined by the equations Ν - Τ- Σ λε ( λ ) , λεσ ...
Page 2031
... arbitrary in 5 a sequence { n } with n → in 5. Since F ( XI.1 ) and F is continuous on H , the inequality ( ii ) shows that FTun → FT . On the other hand , the preceding equation shows that FT = TF , which by ( ii ) , converges to TF ...
... arbitrary in 5 a sequence { n } with n → in 5. Since F ( XI.1 ) and F is continuous on H , the inequality ( ii ) shows that FTun → FT . On the other hand , the preceding equation shows that FT = TF , which by ( ii ) , converges to TF ...
Page 2314
... arbitrary constants and let T be the unbounded operator in L2 ( 0 , 1 ) defined by the formal differential operator and the boundary conditions - ƒ ( 0 ) — k 。 ƒ ' ( 0 ) = 0 , - ƒ ( 1 ) — k1ƒ ' ( 1 ) = 0 . = — ( d / dt ) 2 Then T is a ...
... arbitrary constants and let T be the unbounded operator in L2 ( 0 , 1 ) defined by the formal differential operator and the boundary conditions - ƒ ( 0 ) — k 。 ƒ ' ( 0 ) = 0 , - ƒ ( 1 ) — k1ƒ ' ( 1 ) = 0 . = — ( d / dt ) 2 Then T is 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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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