Linear Operators: Spectral theory |
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Page 1099
... singular matrices , it is sufficient to consider the case in which T is non - singular . Then A = ( TT * ) 1/2 is also non - singular and if U = A − 1T , UU * = A - 1A2A - 1I , then U is unitary , and T AU . Let B。 U - 1AP - 1 . Then ...
... singular matrices , it is sufficient to consider the case in which T is non - singular . Then A = ( TT * ) 1/2 is also non - singular and if U = A − 1T , UU * = A - 1A2A - 1I , then U is unitary , and T AU . Let B。 U - 1AP - 1 . Then ...
Page 1184
... singular integrals . Singular integrals of Hilbert - Calderón- Zygmund type may be shown under suitable hypotheses to map functions satisfying a Hölder condition of exponent 0 < ɛ < 1 into functions of the same sort . Singular integrals ...
... singular integrals . Singular integrals of Hilbert - Calderón- Zygmund type may be shown under suitable hypotheses to map functions satisfying a Hölder condition of exponent 0 < ɛ < 1 into functions of the same sort . Singular integrals ...
Page 1919
... Singular element in a B - algebra IX.1.2 ( 861 ) Singular element in a ring , ( 40 ) non - singular operator , ( 45 ) Singular set function , definition , III.4.12 ( 131 ) derivatives of , III.12.6 ( 214 ) Lebesgue decomposition theorem ...
... Singular element in a B - algebra IX.1.2 ( 861 ) Singular element in a ring , ( 40 ) non - singular operator , ( 45 ) Singular set function , definition , III.4.12 ( 131 ) derivatives of , III.12.6 ( 214 ) Lebesgue decomposition theorem ...
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