Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 = 1 , P = ∞ , and Р = mapping may be determined . For p = 2 , the n - dimensional analogue of ...
... 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 = 1 , P = ∞ , and Р = mapping may be determined . For p = 2 , the n - dimensional analogue of ...
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 + ∞ eixy dx x ε • 00 pixy -ixy -e = lim dx x ∞ sin xy lim 2i dx x ...
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 + ∞ eixy dx x ε • 00 pixy -ixy -e = lim dx x ∞ sin xy lim 2i dx x ...
Page 1047
... integral • + ∞0 81 f ( x ) x - y \ dx instead of ( 3 ) , all our considerations would fail . In the multi - dimensional case the convolution integrals ( 4 ) Q ( x - y ) f ( y ) dy x - yn of the form analyzed by Calderón and Zygmund ...
... integral • + ∞0 81 f ( x ) x - y \ dx instead of ( 3 ) , all our considerations would fail . In the multi - dimensional case the convolution integrals ( 4 ) Q ( x - y ) f ( y ) dy x - yn of the form analyzed by Calderón and Zygmund ...
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