same series converges almost surely at every y and the sum function is strongly continuous in ... tinuous in probability at t = t0 if for all d > 0,. limP(|/(t0 + h, ...
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cludes integrally closed domains (i.e. normal domains) and Gorenstein rings. Broadly speaking, they are commutative noetherian rings in which principal.
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and the series (1) converges in a neighborhood of y = 0. The basic result is that the above problem has small amplitude, periodic solu- tions of the form. (2).
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Since (3ng)-L = conv(3±, gx),. ^i|(3^3)± ^^|(3ng)-L . Let denote the canonical homomor- phism of 21 onto %/$r\%. Then 0 g0(£i) £4>(A). Let Æ be the real con-.
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Let D denote the set of all functions y G L^2 such that D{y is absolutely continuous on .... (a) w G D swc/i tfiaf Diw(a) = a», Dito(b) = ft, i = 0, ⢠⢠-, fc â 1. (b) z E D + ...
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 5, Number 3, Summer 1975
Introduction. In the study of ordinary differential operators the class of formally self-adjoint differential expressions plays an important role. Such expressions generate symmetric operators in the L 2 spaces, and hence the well developed theory of symmetric and particularly self-adjoint operators in Hilbert space (or more generally in Banach spaces) can be applied to study the spectrum of such operators, among other things. The classical definition of formal self-adjointness — see the book by Coddington-Levinson [3, p. 84] —is as follows: consider the nth order differential expression: Ly = pn(/ + pn^"-1)
