Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 81
Page 1036
... converges absolutely provided that λ λ for any k . In view of the fact that λ → 0 it follows from the estimate in ( * ) that the series Σ log ( etwa ( 1-2 ) ) k = 1 converges uniformly and absolutely for each compact set of numbers 2 ...
... converges absolutely provided that λ λ for any k . In view of the fact that λ → 0 it follows from the estimate in ( * ) that the series Σ log ( etwa ( 1-2 ) ) k = 1 converges uniformly and absolutely for each compact set of numbers 2 ...
Page 1420
... converges to zero in the topology of D ( T1 ( t + t ' ) ) . Conversely , let { f } converge to zero in the topology ... converges to zero in H and is bounded in D ( T , ( t ) ) . By hypothesis ( b ) it follows that T1 ( t ' ) h ...
... converges to zero in the topology of D ( T1 ( t + t ' ) ) . Conversely , let { f } converge to zero in the topology ... converges to zero in H and is bounded in D ( T , ( t ) ) . By hypothesis ( b ) it follows that T1 ( t ' ) h ...
Page 1664
... converges unconditionally to F. PROOF . It follows from the Definition 37 of the topology in D ( C ) that it suffices to show that ( 2π ) η Σ F eiLq ( x ) dx L Ф converges unconditionally to F ( q ) for each q in C ( C ) . For any set A ...
... converges unconditionally to F. PROOF . It follows from the Definition 37 of the topology in D ( C ) that it suffices to show that ( 2π ) η Σ F eiLq ( x ) dx L Ф converges unconditionally to F ( q ) for each q in C ( C ) . For any set A ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero