Linear Operators: Spectral operators |
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Page 2325
... asymptotic representation -m §n ~ 2πn + a + z2 + Σ 5 m n − " m = 1 and that the zero E , of M ( u ) in R ( 2 ) has the asymptotic representation ∞ §n ~ 2πn + a +22 + Σ §mn - m , m = 1 where the m and m are certain coefficients . Since ...
... asymptotic representation -m §n ~ 2πn + a + z2 + Σ 5 m n − " m = 1 and that the zero E , of M ( u ) in R ( 2 ) has the asymptotic representation ∞ §n ~ 2πn + a +22 + Σ §mn - m , m = 1 where the m and m are certain coefficients . Since ...
Page 2384
... asymptotic to e iut as too . Since , in contrast to σ1 , such a solution is not uniquely determined by its asymptotic form , we meet a number of additional , slight , technical complications in the asymptotic analysis of such solutions ...
... asymptotic to e iut as too . Since , in contrast to σ1 , such a solution is not uniquely determined by its asymptotic form , we meet a number of additional , slight , technical complications in the asymptotic analysis of such solutions ...
Page 2394
... asymptotic to e - itu as t → ∞ and whose derivative is asymptotic to iμettu as t → ∞ . Then ôз ( t , μ ) = a ( μ ) σ1 ( 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 ) σ1 ( t , μ ) + b ( μ ) σ2 ( t , μ ) for suitable functions a ( μ ) and b ( μ ) . It is evident from the asymptotic ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero