Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 86
Page 1019
... inequality is obvious for n = 1 and may be easily checked for n 2. We shall suppose the inequality to be known for n - 1 , and proceed by induction . If ( a ,, ) is an nxn matrix , let [ a1j , aj , ˇ uj = ... , n , define a set of n ...
... inequality is obvious for n = 1 and may be easily checked for n 2. We shall suppose the inequality to be known for n - 1 , and proceed by induction . If ( a ,, ) is an nxn matrix , let [ a1j , aj , ˇ uj = ... , n , define a set of n ...
Page 1061
... inequality , and the theorem is proved for all p , 1 < p < ∞ . Q.E.D. Having proved the basic inequality of M. Riesz , we now proceed to prove the full inequality of Calderón and Zygmund . Our first step is to put the result of M ...
... inequality , and the theorem is proved for all p , 1 < p < ∞ . Q.E.D. Having proved the basic inequality of M. Riesz , we now proceed to prove the full inequality of Calderón and Zygmund . Our first step is to put the result of M ...
Page 1105
... inequality ( a ) for operators in a d - dimensional Hilbert space . Arguing as in the paragraphs of the proof of Lemma 14 following formula ( 3 ) of that proof , where we proved a bilinear inequality quite similar to our present ...
... inequality ( a ) for operators in a d - dimensional Hilbert space . Arguing as in the paragraphs of the proof of Lemma 14 following formula ( 3 ) of that proof , where we proved a bilinear inequality quite similar to our present ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero