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 2286
For each bounded Borel function g on the plane let Š ( g ) denote the closure of AS ( 9 ) A - 1 . The correspondence 7 : S ( g ) + Š ( 9 ) preserves the operational calculus and - = . 1Ē ( da ) , S O ( Q ) where + E ( e ) = E ( e ) ...
For each bounded Borel function g on the plane let Š ( g ) denote the closure of AS ( 9 ) A - 1 . The correspondence 7 : S ( g ) + Š ( 9 ) preserves the operational calculus and - = . 1Ē ( da ) , S O ( Q ) where + E ( e ) = E ( e ) ...
Page 2320
Throughout this section , Bi , i = 1 , ... , n , will denote a set of n linearly independent boundary values for 7. Thus , by Corollary XIII.2.23 , there exist two n x n matrices such that and Bu dij n - 1 n - 1 ( 1 ) ΒΙ.f ) = Σ αμf ( 0 ) ...
Throughout this section , Bi , i = 1 , ... , n , will denote a set of n linearly independent boundary values for 7. Thus , by Corollary XIII.2.23 , there exist two n x n matrices such that and Bu dij n - 1 n - 1 ( 1 ) ΒΙ.f ) = Σ αμf ( 0 ) ...
Page 2436
Next , let C ( EM ) denote the set of all infinitely often differentiable complex valued functions defined in En and vanishing outside a bounded set , let ge C.
Next , let C ( EM ) denote the set of all infinitely often differentiable complex valued functions defined in En and vanishing outside a bounded set , let ge C.
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 other sections not shown
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero
Bibliographic information
| Title | 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 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |