## Linear Operators: Spectral theory |

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Page 1290

that since to ti - (T211)*, the operator X (–) () to () is formally self adjoint provided

only that the

operator (i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is formally self adjoint provided that

p(t) is ...

that since to ti - (T211)*, the operator X (–) () to () is formally self adjoint provided

only that the

**coefficients**p, are real. In the same way, the formal differentialoperator (i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is formally self adjoint provided that

p(t) is ...

Page 1435

by formally substituting the asymptotic expression for a, in [+3] and comparing

operator on an interval I having

end ...

by formally substituting the asymptotic expression for a, in [+3] and comparing

**coefficients**of z-". Thus, in all cases in which we deal with a formal differentialoperator on an interval I having

**coefficients**analytic in I and with poles at the freeend ...

Page 1486

In the next few paragraphs t denotes a formally self adjoint formal differential

operator of order n, defined on the interval R = {– o – t < -i- oc). Let t have the form

n d j -3.0 (). and suppose that all the

same ...

In the next few paragraphs t denotes a formally self adjoint formal differential

operator of order n, defined on the interval R = {– o – t < -i- oc). Let t have the form

n d j -3.0 (). and suppose that all the

**coefficients**a, are periodic and have thesame ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero