## Linear Operators, Part 2 |

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Page 1278

CHAPTER XIII Ordinary Differential Operators 1. Introduction: Elementary

Properties of

the most important single class of operators are the differential operators. The

study of ...

CHAPTER XIII Ordinary Differential Operators 1. Introduction: Elementary

Properties of

**Formal Differential Operators**From the point of view of applications,the most important single class of operators are the differential operators. The

study of ...

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 if 1;' = (r0r1)", the operator é.<~1>'(§.)¥~<~(§.)' 4 is formally self adjoint

provided only that the coefficients pi are real. In the same way, the

provided ...

that since if 1;' = (r0r1)", the operator é.<~1>'(§.)¥~<~(§.)' 4 is formally self adjoint

provided only that the coefficients pi are real. In the same way, the

**formal****differential operator**(i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is formally self adjointprovided ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma 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