Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2325
... asymptotic representation m §n ~ 2wn + a + z2 + Σ 5 m n − m m = 1 , and that the zero E of M ( u ) in R ( 2 ) has the asymptotic representation . §n Σ } , ~ 2πn + a + z2 + Σ { m n ̄ m = 1 -m > where the m and m are certain coefficients ...
... asymptotic representation m §n ~ 2wn + a + z2 + Σ 5 m n − m m = 1 , and that the zero E of M ( u ) in R ( 2 ) has the asymptotic representation . §n Σ } , ~ 2πn + a + z2 + Σ { m n ̄ m = 1 -m > where the m and m are certain coefficients ...
Page 2394
... asymptotic to e - itu as t → ∞ and whose derivative is asymptotic to iμettu as t → ∞ . Then ôз ( t , μ ) = a ( μ ) ơ1 ( t , μ ) + b ( μ ) σ2 ( t , μ ) for suitable functions a ( μ ) and b ( μ ) . It is evident from the asymptotic ...
... asymptotic to e - itu as t → ∞ and whose derivative is asymptotic to iμettu as t → ∞ . Then ôз ( t , μ ) = a ( μ ) ơ1 ( t , μ ) + b ( μ ) σ2 ( t , μ ) for suitable functions a ( μ ) and b ( μ ) . It is evident from the asymptotic ...
Page 2399
... asymptotic relation- ships Մշ o1 ( t ) ~ 1 , 02 ( t ) ~ t as t → ∞o . : PROOF . We saw in Corollary 2 that σ , ( t ) = σ ( t , 0 ) satisfies the first of these asymptotic relationships . Let a be so large that o1 ( t ) 0 for a too ...
... asymptotic relation- ships Մշ o1 ( t ) ~ 1 , 02 ( t ) ~ t as t → ∞o . : PROOF . We saw in Corollary 2 that σ , ( t ) = σ ( t , 0 ) satisfies the first of these asymptotic relationships . Let a be so large that o1 ( t ) 0 for a too ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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