Linear Operators, Part 2 |
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Page 1178
... vector- valued functions . Let M be the mapping in L ( ↳1⁄2 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function whose nth component has the Fourier transform h ...
... vector- valued functions . Let M be the mapping in L ( ↳1⁄2 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function whose nth component has the Fourier transform h ...
Page 1749
... vector equal to the sum of the " electric " vector and the imaginary unit i times the magnetic vector , and where the matrices A1 , A2 , and A , are given by the formulae A1 0 - ( :-) = 0 A2 = 0 i 0 ( 0 0 0 A3 - -i 0 0 0 i 0 0 0 0 Both ...
... vector equal to the sum of the " electric " vector and the imaginary unit i times the magnetic vector , and where the matrices A1 , A2 , and A , are given by the formulae A1 0 - ( :-) = 0 A2 = 0 i 0 ( 0 0 0 A3 - -i 0 0 0 i 0 0 0 0 Both ...
Page 1849
... vector lattices , I , II . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217-234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . Some general theorems and convergence theorems in vector lattices . J ...
... vector lattices , I , II . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217-234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . Some general theorems and convergence theorems in vector lattices . J ...
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 domain 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 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 tr(T transform unique unitary vanishes vector zero