Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1050
... Lebesgue measurable function f defined on Euclidean n - space E " , supposing that has a finite number of " singularities " at which it is not Lebesgue integrable , and defining a certain Cauchy - type principal value integral for f 1 ...
... Lebesgue measurable function f defined on Euclidean n - space E " , supposing that has a finite number of " singularities " at which it is not Lebesgue integrable , and defining a certain Cauchy - type principal value integral for f 1 ...
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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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