Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 u1 = [ α1j , α2j , ani ] , j 1 ,. ... , 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 u1 = [ α1j , α2j , ani ] , j 1 ,. ... , 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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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