Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 69
Page 2403
We then use this inequality to apply Theorem 1 in an illustrative but somewhat artificial setting , essentially to ... A first application ( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but ...
We then use this inequality to apply Theorem 1 in an illustrative but somewhat artificial setting , essentially to ... A first application ( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but ...
Page 2413
Q.E.D. > Theorem 1 and its corollaries are readily generalized to apply to unbounded operators . 2 8 THEOREM . Let X be a B - space , and let T be a closed , densely defined operator in X , with domain D ( T ) .
Q.E.D. > Theorem 1 and its corollaries are readily generalized to apply to unbounded operators . 2 8 THEOREM . Let X be a B - space , and let T be a closed , densely defined operator in X , with domain D ( T ) .
Page 2434
Applying Theorem 8 and Corollary 9 , the present theorem follows at once . Q.E.D. By using appropriate " diagonalizing " transformations ( cf. Theorem XII.3.16 ) , we may apply Theorem 21 to analyze a variety of operators .
Applying Theorem 8 and Corollary 9 , the present theorem follows at once . Q.E.D. By using appropriate " diagonalizing " transformations ( cf. Theorem XII.3.16 ) , we may apply Theorem 21 to analyze a variety of operators .
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
30 other sections not shown
Other editions - View all
Common terms and phrases
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 contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula 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