Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 - 1 A2A - 1 = I , then U is unitary , and T = AU . Let B。= U - 1Ao1 ...
... 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 - 1 A2A - 1 = I , then U is unitary , and T = AU . Let B。= U - 1Ao1 ...
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
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