Linear Operators: Spectral theory |
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Page 950
... Lebesgue measure : in the case of a compact group , its existence and uniqueness was proved in Theorem 1.1 . The reader who is unfamiliar with Haar measure may wish to consult the remarks under the heading Convolution Algebras in ...
... Lebesgue measure : in the case of a compact group , its existence and uniqueness was proved in Theorem 1.1 . The reader who is unfamiliar with Haar measure may wish to consult the remarks under the heading Convolution Algebras in ...
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 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
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero