Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1684
... derivative of F of order k belongs to L ( E ) , it follows that every partial derivative of F of order not more than m is continuous in the closure of E. + PROOF . By Corollary 2 and Hölder's inequality , each ( k — m ) th derivative of ...
... derivative of F of order k belongs to L ( E ) , it follows that every partial derivative of F of order not more than m is continuous in the closure of E. + PROOF . By Corollary 2 and Hölder's inequality , each ( k — m ) th derivative of ...
Page 1687
... derivatives of order not more than k belong to L ( E ) . By Lemma 3 , ( h , F ) 0q - 1 and all its derivatives of order not more than m are continuous in the closure of V. From this and Lemma 3.47 it is evident that h¡F ( h , F ) oq ...
... derivatives of order not more than k belong to L ( E ) . By Lemma 3 , ( h , F ) 0q - 1 and all its derivatives of order not more than m are continuous in the closure of V. From this and Lemma 3.47 it is evident that h¡F ( h , F ) oq ...
Page 1727
... derivatives if one of x1 , ... , xn is zero and if -k ≤ min ( L ) ≤ max ( L ) ≤ k - 1 . In the same way we see , using ( 6 ) and ( 7 ) , that SL vanishes together with all its derivatives of order at most j if one of x1 ,. ... , xn ...
... derivatives if one of x1 , ... , xn is zero and if -k ≤ min ( L ) ≤ max ( L ) ≤ k - 1 . In the same way we see , using ( 6 ) and ( 7 ) , that SL vanishes together with all its derivatives of order at most j if one of x1 ,. ... , xn ...
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