Linear Operators: Spectral theory |
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Page 1178
... valued functions into the space L2 ( l2 ) of square - integrable vector - valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , X maps the space L K of scalar - valued functions boundedly into the space L ( 2 ) ...
... valued functions into the space L2 ( l2 ) of square - integrable vector - valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , X maps the space L K of scalar - valued functions boundedly into the space L ( 2 ) ...
Page 1751
Nelson Dunford, Jacob T. Schwartz. differentiable m - vector valued functions defined in C1 . Similarly , Ĉ ( C1 ) and Ĉ ( C1 ) will denote the subspaces of Ĉ ( C1 ) consisting of all functions which are multiply periodic of period 27 ...
Nelson Dunford, Jacob T. Schwartz. differentiable m - vector valued functions defined in C1 . Similarly , Ĉ ( C1 ) and Ĉ ( C1 ) will denote the subspaces of Ĉ ( C1 ) consisting of all functions which are multiply periodic of period 27 ...
Page 1786
... vector - 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 ...
... vector - 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 ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero