Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 63
Page 1634
... derivatives . This task may be regarded as being solved by the definitions customary in Laurent Schwartz ' theory of distributions , to which Section 3 below will be devoted . Once generalized derivatives in the sense of the theory of ...
... derivatives . This task may be regarded as being solved by the definitions customary in Laurent Schwartz ' theory of distributions , to which Section 3 below will be devoted . Once generalized derivatives in the sense of the theory of ...
Page 1638
... derivatives of order not more than k exists and is continuous . The sets Co ( I ) and C ( I ) consist of those ... derivative has a continuous extension to I. If this is the case , f ( x ) is defined for x in I and J ≤k as the extension ...
... derivatives of order not more than k exists and is continuous . The sets Co ( I ) and C ( I ) consist of those ... derivative has a continuous extension to I. If this is the case , f ( x ) is defined for x in I and J ≤k as the extension ...
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 , ... , xn is ...
... 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 , ... , xn is ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero