Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 81
Page 1297
... norm of ƒ as an element of H " ( J ) it follows easily that D ( T , ( T ) ) is also complete under the norm f2 . As f≤f it follows from Theorem II.2.5 that the two norms are equivalent . The lemma follows immediately from this ...
... norm of ƒ as an element of H " ( J ) it follows easily that D ( T , ( T ) ) is also complete under the norm f2 . As f≤f it follows from Theorem II.2.5 that the two norms are equivalent . The lemma follows immediately from this ...
Page 1431
... norm of D ( T1 ( t ' ) ) . ( e ) The closure of D ( T。( τ ′ ) ) in the norm of D ( T1 ( t ' ) ) coincides with the closure of D ( To ( t ' ) ) in the norm of D ( T1 ( t ) ) . 1 Let D1 and D2 be the closures of D ( To ( 7 ' ) ) in the norms ...
... norm of D ( T1 ( t ' ) ) . ( e ) The closure of D ( T。( τ ′ ) ) in the norm of D ( T1 ( t ' ) ) coincides with the closure of D ( To ( t ' ) ) in the norm of D ( T1 ( t ) ) . 1 Let D1 and D2 be the closures of D ( To ( 7 ' ) ) in the norms ...
Page 1639
... norm equivalent to the norm displayed , though not under the norm displayed itself . It is in the sense of these norms that we speak of the topology of C ( I ) , C ( I ) , etc. If is a formal partial differential operator of the form τ ...
... norm equivalent to the norm displayed , though not under the norm displayed itself . It is in the sense of these norms that we speak of the topology of C ( I ) , C ( I ) , etc. If is a formal partial differential operator of the form τ ...
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