Linear Operators: Spectral operators |
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Page 2284
... suppose that B is itself complete and satisfies the countable chain condition . Both these properties hold for B if ... suppose the sets en are disjoint and U - 1 en P , the whole plane . n - סא n ... " x * Now consider n fixed and ...
... suppose that B is itself complete and satisfies the countable chain condition . Both these properties hold for B if ... suppose the sets en are disjoint and U - 1 en P , the whole plane . n - סא n ... " x * Now consider n fixed and ...
Page 2303
... Suppose that E is its resolution of the identity , and suppose that { n } is an enumeration of its spectrum . Let d , denote the distance from λ to o ( T ) - { \ n } . Suppose that for all but a finite number of n , E ( λ ) has a one ...
... Suppose that E is its resolution of the identity , and suppose that { n } is an enumeration of its spectrum . Let d , denote the distance from λ to o ( T ) - { \ n } . Suppose that for all but a finite number of n , E ( λ ) has a one ...
Page 2362
... Suppose that all but a finite number of the points in o ( T ' ) are simple poles of the resolvent function R ( λ ; T ) ; let { U } be a sequence of bounded domains covering the entire plane , such that lim , minge v1 | 2 | Ui = ∞ . It ...
... Suppose that all but a finite number of the points in o ( T ' ) are simple poles of the resolvent function R ( λ ; T ) ; let { U } be a sequence of bounded domains covering the entire plane , such that lim , minge v1 | 2 | Ui = ∞ . It ...
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