## Linear Operators, Part 2 |

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Page 1503

Examples We now wish to illustrate the application of the preceding theory to

specific

past few sections, he will find it evident that in applying the general methods to ...

Examples We now wish to illustrate the application of the preceding theory to

specific

**differential equations**. If the reader surveys the theory developed in thepast few sections, he will find it evident that in applying the general methods to ...

Page 1528

The first of these algebraic equations, which is simply the characteristic equation

of the

irregular ...

The first of these algebraic equations, which is simply the characteristic equation

of the

**differential equation**, ... + c**—"z>}z-~/. f being a solution of the original**differential equation**Lf = 0, we find that L')" has rational coefficients, and anirregular ...

Page 1629

CHAPTER XIV Linear Partial

The Cauchy Problem, Local Dependence In this chapter, we shall discuss a

variety of theorems having to do with linear partial differential operators. Since

the ...

CHAPTER XIV Linear Partial

**Differential Equations**and Operators l. IntroductionThe Cauchy Problem, Local Dependence In this chapter, we shall discuss a

variety of theorems having to do with linear partial differential operators. Since

the ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

13 other sections not shown

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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