Linear Operators: Spectral theory |
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Page 1165
... extended to vector - valued functions , a real - variable proof of the sort given by Calderón and Zygmund [ 1 ] can be so extended . We indicate here how to take systematic ad- vantage of this fact . We will find that we obtain ...
... extended to vector - valued functions , a real - variable proof of the sort given by Calderón and Zygmund [ 1 ] can be so extended . We indicate here how to take systematic ad- vantage of this fact . We will find that we obtain ...
Page 1907
... valued , defini- tion , III.1.11 ( 100-101 ) Euclidean space , definition , IV.2.1 ( 238 ) further properties , IV.15 ( 374 ) study of , IV.3 Euler - Gauss , hypergeometric equa- tion of , XIII.8 ( 1509 ) Extended real and complex numbers ...
... valued , defini- tion , III.1.11 ( 100-101 ) Euclidean space , definition , IV.2.1 ( 238 ) further properties , IV.15 ( 374 ) study of , IV.3 Euler - Gauss , hypergeometric equa- tion of , XIII.8 ( 1509 ) Extended real and complex numbers ...
Page 1917
... value , definition , ( 606 ) Q Quasi - equicontinuity , for bounded functions , IV.6.28 ... Real numbers , extended , ( 3 ) topology of , ( 11 ) Real part , of a ... valued ( 350 ) measure , IV.13.75 Regular singularity of a differential ...
... value , definition , ( 606 ) Q Quasi - equicontinuity , for bounded functions , IV.6.28 ... Real numbers , extended , ( 3 ) topology of , ( 11 ) Real part , of a ... valued ( 350 ) measure , IV.13.75 Regular singularity of a differential ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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