Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 80
Page 1045
... integral ( 1 ) exists for almost all , and defines a bounded mapping of L , ( E " ) into itself , 1≤poo . For p = 2 , the exact norm of this mapping may be determined . For p = 2 , the n - dimensional analogue of Theorem 3.21 ( d ) ...
... integral ( 1 ) exists for almost all , and defines a bounded mapping of L , ( E " ) into itself , 1≤poo . For p = 2 , the exact norm of this mapping may be determined . For p = 2 , the n - dimensional analogue of Theorem 3.21 ( d ) ...
Page 1046
Nelson Dunford, Jacob T. Schwartz. an integral studied by Hilbert . The integral ( 2 ) may be interpreted in terms of a Cauchy principal value as • + ∞0 pixy ∞- x dx = lim 04-3 = lim eixy dx x C + 0 = 8∞ eixy - e - ixy x dx - lim 2i S ...
Nelson Dunford, Jacob T. Schwartz. an integral studied by Hilbert . The integral ( 2 ) may be interpreted in terms of a Cauchy principal value as • + ∞0 pixy ∞- x dx = lim 04-3 = lim eixy dx x C + 0 = 8∞ eixy - e - ixy x dx - lim 2i S ...
Page 1047
... integral • + ∞0 ∞- f ( x ) dx | x − y | instead of ( 3 ) , all our considerations would fail . In the multi - dimensional case the convolution integrals ( 4 ) + ∞0 ∞- Q ( x - y ) | x - yn f ( y ) dy of the form analyzed by Calderón ...
... integral • + ∞0 ∞- f ( x ) dx | x − y | instead of ( 3 ) , all our considerations would fail . In the multi - dimensional case the convolution integrals ( 4 ) + ∞0 ∞- Q ( x - y ) | x - yn f ( y ) dy of the form analyzed by Calderón ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
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