Feb 8, 1973 - toM- N, is [M,N] + R(z). From the above facts, it can be proved that the diagonal (M = N). P.A. to the homographically transformed operator (AT + ...
Aug 14, 1991 - The series in Theorem B diverges pointwise. .... Proposition 3.20 of [BJR2] (or by direct computation) that ...... UNIVERSITY OF MISSOURI. ST.
Littlewood-Paley and multiplier theory, by R. E. Edwards and G. I. Gaudry, .... showed that Æ and s(f) have equivalent L2 norms for each such 8. In complete analogy ..... A. M. Garsia, Martingale inequalities, Benjamin, New York, 1973. 10. S.
method is based upon a general method due to G. M. Goluzin [l], and consists of ... announce the solutions to certain general extremal problems for Vk*.
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 + ...
Aug 22, 1974 - DANIEL B. SHAPIRO AND JOSEPH A. WOLF. Let F be a field R ... Since e 3J) -(e + f) + 2(e J)), the orthogonal projection ra: X. B sends xt to et ...
of India under the bilateral India-Slovenia grants BI-IN/06-07-002 and ... Work supported by the University Grants Commission (UGC), Govt of India under ...
Sep 20, 1984 - for some lower triangular non-singular matrix Bnh and a formal power series. CO. (1-2). Ax) = Zfnx", n=Q find constants ak such that. CO. (1.3).
Now, ac"1 and be'1 commute and actually they generate a subgroup H ..... [Chi] C. Champetier, Cocroissance des groupes a petite simplification, Bull. London.
Pamela B. Pierce, Department of Mathematical Sciences, The College of. Wooster ... Daniel Waterman, Department of Mathematics, Florida Atlantic University,.
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, ...
Born Series for Two, Three, and Four Particle Scattering. 79 k'esuppg implies ..... Within these blocks, we will show that each entry, except for the z independent ...
Let (X,d)be a metric space, call ÎÎ(X, ε) the minimum number of balls of d-radius ε ... Hausdorff Dimension of Hyperbolic Sets of Diffeomorphisms and Flows. We recall the .... on B(0x, r), the ball of center zero and radius r in Ex and maps into
John Z. Imbrie**. Department of ... National Science Foundation predoctoral fellow, 1979-80. Currently ..... depending on p,η, C such that for R of the form (4.3.2),.
generalized exponential growth model 5.0 , observe that, at the point x G 0,. 1. ¡. ¦ x . . T . v. f x, , a ,. f x, , a s x exp y x s Ag x,. ,. Ž . Ž . Ž . Ž . ny1. T x ž. / a ny1 jq1 y.
"smooth" Z-norm at the stage i) means that low Fourier modes (in x) of the ..... Take any x £ Tn. Multiplying (1.1) by ΰ(t,x) and taking the imaginary part we get.
formly positive definite, i.e., there exists ,> 0 such that for all x. R", } R and > 0, ... valid uniformly in u only when u belongs to the class of nonnegative solutions which vanish .... tive solutions of second-orderelliptic equations which vanish
Stanford University .... For any two indices i and V, the difference of the deleted sample values S^ .... Define S+* = ¿ Si«, and notice that ES+
Universite Pierre et Marie Curie, Laboratoire de Calcul Probabilites, F-75230 Paris, France. Abstract. An Ising model traditionally is a model for a repartition of ...
As an offshoot of the proof one obtains an essentially coordinate-free algorithm for ... space X from those living in the compactification X. On X9 we are also given ...
been periodically noticed [2] [3] [4] that this statement is rigorously proved only ... line, a factor Bt for each reduction vertex and a factor (â λ) for each ordinary.
regularized Euclidean Yang-Mills theory via a well defined functional integral. ... (weak) Riemannian structure in formal Faddeev-Popov path integral is clearly.
Department of Applied Physics, Waseda University, Tokyo 160, Japan. 2. Research ... Abstract. We consider the time-dependent SchrÏdinger-Hartree equation.
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).
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 6, Number 4, Fall 1976
PERIODIC SOLUTIONS TO A WAVE EQUATION J . M . GREENBERG 1
ABSTRACT. The problem is to establish the existence of small amplitude, time periodic solutions of
(WE) v
'
(BC)
^-±a(^L) 2
dt
dx
= o,
0 < x < l and
\ dx I
u(0, t) = «(1, t) = 0,
where a(y) = y 3(l + S a n y 2 «)
(1)
n=l
and the series (1) converges in a neighborhood of y = 0. The basic result is that the above problem has small amplitude, periodic solutions of the form (2)
