Linear Operators: Spectral operators |
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Page 1933
... resolvent of a bounded spectral operator have a number of important properties not enjoyed by functions of the form R ( § ; T ) x when T is not a spectral operator ... RESOLVENT OF A SPECTRAL OPERATOR The Resolvent of a Spectral Operator.
... resolvent of a bounded spectral operator have a number of important properties not enjoyed by functions of the form R ( § ; T ) x when T is not a spectral operator ... RESOLVENT OF A SPECTRAL OPERATOR The Resolvent of a Spectral Operator.
Page 2291
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION . An operator T is discrete if there is a number λ in its resolvent set ...
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION . An operator T is discrete if there is a number λ in its resolvent set ...
Page 2316
... resolvent . By Lemma 8 , the condition for this is ( ❤n , n ) = 0 , where a solution of is - ( T * — X2 1 * ) $ n = 0 . Since by Theorems XIII.2.10 and XII.4.28 , T * is defined by the formal differential operator ( d / dt ) 2 and the ...
... resolvent . By Lemma 8 , the condition for this is ( ❤n , n ) = 0 , where a solution of is - ( T * — X2 1 * ) $ n = 0 . Since by Theorems XIII.2.10 and XII.4.28 , T * is defined by the formal differential operator ( d / dt ) 2 and the ...
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