## Linear Operators: Spectral theory |

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Page 1310

Then the boundary conditions are real, and there is exactly one solution <p(t, X)

of {r—X)q} = 0

, and exactly one solution ip(t, X) of (t — X)y> = 0

Then the boundary conditions are real, and there is exactly one solution <p(t, X)

of {r—X)q} = 0

**square**-**integr able**at a and satisfying the boundary conditions at a, and exactly one solution ip(t, X) of (t — X)y> = 0

**square**-**integrable**at b and ...Page 1329

conditions at a, and exactly one solution y>(t, X) of (r— X)a = 0

at b satisfying the boundary conditions at b. The resolvent 'J* R(X\ T) is an

integral operator whose kernel K(t, s; X) is given by "^J formula [*]. Ģi$ Proof.

conditions at a, and exactly one solution y>(t, X) of (r— X)a = 0

**square**-**integrable**at b satisfying the boundary conditions at b. The resolvent 'J* R(X\ T) is an

integral operator whose kernel K(t, s; X) is given by "^J formula [*]. Ģi$ Proof.

Page 1557

(X— r)f = 0 has a solution which is not

G20 (Wintner). Suppose that q is bounded below, and suppose that X does not ...

(X— r)f = 0 has a solution which is not

**square**-**integrable**but has a**square**-**integrable**derivative. Prove that the point X belongs to the essential spectrum of t.G20 (Wintner). Suppose that q is bounded below, and suppose that X does not ...

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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