Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 74
Page 1660
... subset of I. Let I be an open subset of C. We shall write f⇒ ƒ in I if f f are in Co ( I ) , if all the functions f vanish outside a fixed compact subset of I , and if ƒ → f in the topology of C °° ( I ) as n → ∞ . We may then make ...
... subset of I. Let I be an open subset of C. We shall write f⇒ ƒ in I if f f are in Co ( I ) , if all the functions f vanish outside a fixed compact subset of I , and if ƒ → f in the topology of C °° ( I ) as n → ∞ . We may then make ...
Page 1663
... subset I。 of I whose closure is compact and contained in I will be denoted by A- ( I ) . 36 DEFINITION . Let I be an open subset of C. Let k be an integer , positive or negative . Let { I } , m ≥ 1 , be a sequence of open subsets of I ...
... subset I。 of I whose closure is compact and contained in I will be denoted by A- ( I ) . 36 DEFINITION . Let I be an open subset of C. Let k be an integer , positive or negative . Let { I } , m ≥ 1 , be a sequence of open subsets of I ...
Page 1695
... subset I of E " . Let { I } be a sequence of open subsets of I whose union is I , such that Im is compact and contained in I , and such that ImÏ „ = $ unless | m - p = 1. Then F may be written as the sum F Σ = 1 Fm of a convergent ...
... subset I of E " . Let { I } be a sequence of open subsets of I whose union is I , such that Im is compact and contained in I , and such that ImÏ „ = $ unless | m - p = 1. Then F may be written as the sum F Σ = 1 Fm of a convergent ...
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