Linear Operators, Part 2 |
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Page 1051
... evident from Definition 1. Statements ( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae Sg . P ( x ) dx = gm P ( Ux ) dx , En En -n √gn P ( xx ) dx = | x | ̄ ” √gn P ( x ) dx , En Ф. which are valid for ...
... evident from Definition 1. Statements ( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae Sg . P ( x ) dx = gm P ( Ux ) dx , En En -n √gn P ( xx ) dx = | x | ̄ ” √gn P ( x ) dx , En Ф. which are valid for ...
Page 1347
... evident advantage that it makes o , ( , λ ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . Suppose , for example , that we study the self adjoint operator T ...
... evident advantage that it makes o , ( , λ ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . Suppose , for example , that we study the self adjoint operator T ...
Page 1661
... evident , and instead of giving detailed statements which apply to our new context we shall simply refer to " Lemma 6 , " etc. , as " generalized to D „ ( I ) ” when necessary . Lemma 10 applies similarly in an evident way to the new ...
... evident , and instead of giving detailed statements which apply to our new context we shall simply refer to " Lemma 6 , " etc. , as " generalized to D „ ( I ) ” when necessary . Lemma 10 applies similarly in an evident way to the new ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero