Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1178
... valued functions into the space L2 ( 12 ) of square - integrable vector - valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , maps the space L , of scalar - valued functions boundedly into the space L ( 2 ) ...
... valued functions into the space L2 ( 12 ) of square - integrable vector - valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , maps the space L , of scalar - valued functions boundedly into the space L ( 2 ) ...
Page 1179
... valued function with the Fourier transform f ( ) into the vector - valued function whose nth component has the Fourier transform fn ( ) defined by ( 65 ) fn ( § ) = ƒ ( § ) , 2 " ≤ § < 2n + 1 , = 0 , otherwise , is a bounded map of L ...
... valued function with the Fourier transform f ( ) into the vector - valued function whose nth component has the Fourier transform fn ( ) defined by ( 65 ) fn ( § ) = ƒ ( § ) , 2 " ≤ § < 2n + 1 , = 0 , otherwise , is a bounded map of L ...
Page 1786
... valued functions . Studia Math . 11 , 185–196 ( 1950 ) . Continuity of vector - valued functions of bounded variation . Studia Math . 12 , 133-142 ( 1951 ) . On some theorems of S. Saks . Studia Math . 13 , 18-29 ( 1953 ) . A theorem on ...
... valued functions . Studia Math . 11 , 185–196 ( 1950 ) . Continuity of vector - valued functions of bounded variation . Studia Math . 12 , 133-142 ( 1951 ) . On some theorems of S. Saks . Studia Math . 13 , 18-29 ( 1953 ) . A theorem on ...
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