## Linear Operators: Spectral theory |

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Page 860

A S-

a fi-

*, (xy)* = i/*a:* (our)* = ax*, (x*)* = x. All of the examples mentioned above, with ...

A S-

**algebra**X is commutative in case xy = yx for all x and y in X. An involution ina fi-

**algebra**X is a mapping x -> x* of X into itself with the properties (*+«/)* = x*+y*, (xy)* = i/*a:* (our)* = ax*, (x*)* = x. All of the examples mentioned above, with ...

Page 866

We recall that if 3 is a two-sided ideal in the

form an

(our)+3, (*+3)(y+3) = (**)+3. This

We recall that if 3 is a two-sided ideal in the

**algebra**X, the cosets a; +3, x e Xform an

**algebra**under the following definitions (^+3) + (2/+3) = (* + 2/)+3 a(^+3) =(our)+3, (*+3)(y+3) = (**)+3. This

**algebra**is the quotient**algebra**of £ by 3 and is ...Page 979

One of these algebras, namely the

met before. For convenience, its definition and some of its properties will be

restated here. For every / in L^R) the convolution (/ * «)(*) = \Rf(x-y)g{y)dy, g e L2(

R), ...

One of these algebras, namely the

**algebra**2T of the preceding section, we havemet before. For convenience, its definition and some of its properties will be

restated here. For every / in L^R) the convolution (/ * «)(*) = \Rf(x-y)g{y)dy, g e L2(

R), ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero