Linear Operators: Spectral operators |
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Page 2325
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero En of M ( u ) in R has the asymptotic representation m - §n ~ 2πn + a + z 2 + Σ 5mn - m , m = 1 and that the zero έ of M ...
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero En of M ( u ) in R has the asymptotic representation m - §n ~ 2πn + a + z 2 + Σ 5mn - m , m = 1 and that the zero έ of M ...
Page 2330
... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n 2πί 0 n - Ĉ Axs ( μ + 2πn ) e1a + Aks ( μ + 2πn ) e ̄1a + A ′′ , ( μ + 2πn ) } k , j = 1 A ( μμ + 2πn ) etu + A ' ( μ + 2πn ) e - 1 " + A " ( μ + 2πn ) ...
... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n 2πί 0 n - Ĉ Axs ( μ + 2πn ) e1a + Aks ( μ + 2πn ) e ̄1a + A ′′ , ( μ + 2πn ) } k , j = 1 A ( μμ + 2πn ) etu + A ' ( μ + 2πn ) e - 1 " + A " ( μ + 2πn ) ...
Page 2341
... formula ( 58 ) , that the family of all sums MEJ E. m J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G1 that if we excise from the angle A1 of the μ ...
... formula ( 58 ) , that the family of all sums MEJ E. m J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G1 that if we excise from the angle A1 of the μ ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero