## Linear Operators: Spectral theory |

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Page 1280

A

the complex-valued functions a{, called the coefficient functions, belong to C°°(/),

and such that the function an, called the leading coefficient, is not zero at any ...

A

**formal differential operator**of order n on the interval / is an expression such thatthe complex-valued functions a{, called the coefficient functions, belong to C°°(/),

and such that the function an, called the leading coefficient, is not zero at any ...

Page 1289

Q.E.D. A number of other principles belonging to the formal algebra of

of them; for this reason they will not be numbered as theorems and lemmas.

Q.E.D. A number of other principles belonging to the formal algebra of

**formal****differential operators**are worth mentioning although we shall not make much useof them; for this reason they will not be numbered as theorems and lemmas.

Page 1290

that since r*r* = (tjTj)*, the operator is formally self adjoint provided only that the

coefficients pf are real. In the same way, the

n{p(t)(dldt) + (dldt)p(t)}(dldt)n is formally self adjoint provided that p(t) is a real ...

that since r*r* = (tjTj)*, the operator is formally self adjoint provided only that the

coefficients pf are real. In the same way, the

**formal differential operator**(il2)(d[dt)n{p(t)(dldt) + (dldt)p(t)}(dldt)n is formally self adjoint provided that p(t) is a real ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero