Linear Operators, Part 2 |
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Page 1050
... Lebesgue measurable function f defined on Euclidean n - space E " , supposing that ƒ has a finite number of " singularities " at which it is not Lebesgue integrable , and defining a certain Cauchy - type principal value integral for f ...
... Lebesgue measurable function f defined on Euclidean n - space E " , supposing that ƒ has a finite number of " singularities " at which it is not Lebesgue integrable , and defining a certain Cauchy - type principal value integral for f ...
Page 1801
... Lebesgue - Nikodým . Ann . of Math . ( 2 ) 42 , 547–555 ( 1941 ) . Sur le théorème de Lebesgue - Nikodym , II . Bull . Soc . Math . France 72 , 193-239 ( 1944 ) ; errata , ibid . , 74 , 66-68 ( 1946 ) . 6. Complex structures on real ...
... Lebesgue - Nikodým . Ann . of Math . ( 2 ) 42 , 547–555 ( 1941 ) . Sur le théorème de Lebesgue - Nikodym , II . Bull . Soc . Math . France 72 , 193-239 ( 1944 ) ; errata , ibid . , 74 , 66-68 ( 1946 ) . 6. Complex structures on real ...
Page 1913
... Lebesgue and Lebesgue - Stieltjes , ( 143 ) Lebesgue extension of , III.5.18 ( 143 ) outer , III.5.3 ( 133 ) positive matrix , XIII.5.12 ( 1349 ) -preserving transformation , ( 667 ) product , III.11 Radon , ( 142 ) regular vector ...
... Lebesgue and Lebesgue - Stieltjes , ( 143 ) Lebesgue extension of , III.5.18 ( 143 ) outer , III.5.3 ( 133 ) positive matrix , XIII.5.12 ( 1349 ) -preserving transformation , ( 667 ) product , III.11 Radon , ( 142 ) regular vector ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero