Linear Operators: Spectral theory |
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Page 1058
... u - integrable on S. The Fubini theorem gives - -log x1 | | x | n - 1 and so [ _q ( w ) μ ( do ) = 2 dx = S dr { S1 - log r - log ( w ) , | ) μ ( dos ) } , -log | x1 | dx + 2μ ( S ) Slog log ( r ) dr , S and it suffices to prove that ...
... u - integrable on S. The Fubini theorem gives - -log x1 | | x | n - 1 and so [ _q ( w ) μ ( do ) = 2 dx = S dr { S1 - log r - log ( w ) , | ) μ ( dos ) } , -log | x1 | dx + 2μ ( S ) Slog log ( r ) dr , S and it suffices to prove that ...
Page 1170
... u to denote the L1 - norm of the integrable function u . Lemma 16 is proved by Hörmander ( loc . cit . ) for scalar- valued functions . The proof for vector - valued functions is hardly different . We therefore omit the proof , and pass ...
... u to denote the L1 - norm of the integrable function u . Lemma 16 is proved by Hörmander ( loc . cit . ) for scalar- valued functions . The proof for vector - valued functions is hardly different . We therefore omit the proof , and pass ...
Page 1341
... u . If { m } is the matrix of densities of μ , with respect to μ , then there exist non- negative u - measurable functions q1 , i = 1 , ... , n , u - integrable over each bounded interval , and u - measurable functions a ,,, 1 ≤ i , j ...
... u . If { m } is the matrix of densities of μ , with respect to μ , then there exist non- negative u - measurable functions q1 , i = 1 , ... , n , u - integrable over each bounded interval , and u - measurable functions a ,,, 1 ≤ i , j ...
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