Linear Operators, Part 2 |
From inside the book
Results 1-3 of 50
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 ) 0q ...
... 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 ) 0q ...
Page 1727
... derivatives if one of 1 , ... , 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 , .. x is zero ...
... derivatives if one of 1 , ... , 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 , .. x is zero ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero