Linear Operators, Part 2 |
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Page 2038
... independent of t and thus also independent of u . By letting u → t + we have - [ = q1 - T ( t ) q ( 0 ) , 0 < t < ∞ , - p and by letting t → 0 + we see that = p ( 0 ) ( 0 ) = 0 . This shows that P1 = T ( t ) q ( 0 ) = p ( t ) and ...
... independent of t and thus also independent of u . By letting u → t + we have - [ = q1 - T ( t ) q ( 0 ) , 0 < t < ∞ , - p and by letting t → 0 + we see that = p ( 0 ) ( 0 ) = 0 . This shows that P1 = T ( t ) q ( 0 ) = p ( t ) and ...
Page 2327
... independent solutions p1 , p2 of the equation 7 = λop such that B1 ( 91 ) = P1 , P2 Ф B ( 92 ) = 0 , i = 1 , ... , k . Then 1 may be represented uniquely as P1 Σ ¦ = 1C1 , σ , ( μ ( X ) ) and , similarly , 92 = Σ } = 1 © 2 ; σ ; ( μ ...
... independent solutions p1 , p2 of the equation 7 = λop such that B1 ( 91 ) = P1 , P2 Ф B ( 92 ) = 0 , i = 1 , ... , k . Then 1 may be represented uniquely as P1 Σ ¦ = 1C1 , σ , ( μ ( X ) ) and , similarly , 92 = Σ } = 1 © 2 ; σ ; ( μ ...
Page 2439
... independent of ɛ , we have n ( 30 ) | V ( k ) | + ( * ) + Σ 22 р 1.5 = 1 | Ok , ok , ( k ) Mε ( 1+ | k | n + 1 ) − 1 , ар 1 = 1 | Ək1 Let us now note that there exists a positive absolute constant c such that ( 31 ) | w - xw ' | ≥ c ...
... independent of ɛ , we have n ( 30 ) | V ( k ) | + ( * ) + Σ 22 р 1.5 = 1 | Ok , ok , ( k ) Mε ( 1+ | k | n + 1 ) − 1 , ар 1 = 1 | Ək1 Let us now note that there exists a positive absolute constant c such that ( 31 ) | w - xw ' | ≥ c ...
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