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Page 1173
... Let Q ( x ) be a numerically - valued kernel defined in E " , homogeneous of order 0 , smooth except at x = 0 , and whose surface integral over the surface of the unit sphere is zero . Let L ( La ) denote the L - space of functions ...
... Let Q ( x ) be a numerically - valued kernel defined in E " , homogeneous of order 0 , smooth except at x = 0 , and whose surface integral over the surface of the unit sphere is zero . Let L ( La ) denote the L - space of functions ...
Page 1557
... q is bounded below , and suppose that does not belong to the essential spectrum of 7. Let ƒ be a square - integrable solution of the equation ( 2–7 ) ƒ = 0 , and let g be a second solution of the same equation such that fg ' - f'g ( a ) Let ...
... q is bounded below , and suppose that does not belong to the essential spectrum of 7. Let ƒ be a square - integrable solution of the equation ( 2–7 ) ƒ = 0 , and let g be a second solution of the same equation such that fg ' - f'g ( a ) Let ...
Page 1677
... Let k p≥0 . Let F be in H ) ( C ) , and a F be in H ( C ) . Let G denote an arbitrary element of H ( C ) . Then , by Definition 35 , and by the Hahn - Banach theorem ( II.3.11 ) , the mapping p → G ( q ) can be extended to a ...
... Let k p≥0 . Let F be in H ) ( C ) , and a F be in H ( C ) . Let G denote an arbitrary element of H ( C ) . Then , by Definition 35 , and by the Hahn - Banach theorem ( II.3.11 ) , the mapping p → G ( q ) can be extended to 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