Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 984
... vanishes in a neighborhood of infinity is dense in L1 ( R ) . PROOF . It follows from Lemma 3.6 that the set of all functions in L2 ( R , B , μ ) which vanish outside of compact sets is dense in this space , and from the Plancherel ...
... vanishes in a neighborhood of infinity is dense in L1 ( R ) . PROOF . It follows from Lemma 3.6 that the set of all functions in L2 ( R , B , μ ) which vanish outside of compact sets is dense in this space , and from the Plancherel ...
Page 997
... vanishes on U for every † in L1 ( R ) ~ L2 ( R ) whose transform vanishes on the complement of V. PROOF . If moo ( q ) then there is a neighborhood V of the identity in R and a neighborhood U of m , such that Un ( o ( p ) + V + V ) is ...
... vanishes on U for every † in L1 ( R ) ~ L2 ( R ) whose transform vanishes on the complement of V. PROOF . If moo ( q ) then there is a neighborhood V of the identity in R and a neighborhood U of m , such that Un ( o ( p ) + V + V ) is ...
Page 1651
... vanishes outside K , then it is clear that pyk vanishes outside a compact subset of I - Cp ; thus G ( q ) = F ( x ) = 0 . This shows that CGC Cp , and it is clear conversely that CF = CGI CCG . This completes the proof of the existence ...
... vanishes outside K , then it is clear that pyk vanishes outside a compact subset of I - Cp ; thus G ( q ) = F ( x ) = 0 . This shows that CGC Cp , and it is clear conversely that CF = CGI CCG . This completes the proof of the existence ...
Contents
IX | 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 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