## Linear Operators: Spectral theory |

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Page 1310

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

of (t— k)<p = 0

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

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

of (t— k)<p = 0

**square**-**integrable**at a and satisfying the boundary conditions at a,and exactly one solution ip(t, X) of (t— X)tp = 0

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

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

of (t— X)a = 0

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

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

of (t— X)a = 0

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

**square**-**integrable**at b satisfying ...Page 1557

(A— t)/ = 0 has a solution which is not

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

(A— t)/ = 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 z. G20 (Wintner). Suppose that q is bounded below, and suppose that X does not ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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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