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.
Institute for Theoretical Physics, SUNY at Stony Brook, NY 11794-3840, USA ... gives a representation of the time independent correlator (Ï(x2)Ψ + (*ι)y as a.
theory and it is shown that the time-ordered functions and S-matrix elements ... connection between Schwinger functions and time-ordered products is given and.
Department of Mathematics, University of California, Santa Cruz, CA 95064, USA .... following proposition is basic (see e.g., Trautman [1980], or Fischer [1985]). 1.1. ...... 64, for the calculation), so that. IÏo(L(Sn))xCGLin)(SO(n)). Let R*=R-{0}.
intersections of a walk led to many new concepts; the most useful one seems to .... to remember that, in general, small Greek letters are used to denote measures ...
Sep 26, 1986 - to compute the number (fs{G) of ordered s-tuples of elements which ... the poset C(G) of conjugacy classes of subgroups of G had already been ...... 631-636. 9. Peter F. Garst, Cohen-Macaulay Complexes and group actions, ...
rett and Liggett (1983), Guivarc'h (1990) and Holley and Waymire (1992). In particular, by Theorems 1 and 2 of ...... Wiley, New York. [4] Dembo, A. and Zeitouni, ...
Let ffl be a separable Hubert space, and N a positive, self-adjoint operator on 2tf satisfying ..... which requires only information on Euclidean Green's functions.
Ising model and the Field Theory case studied respectively in [1, 2]. In the Ising .... We define new variables r\ by ri = 1 â ^-^) or r\ = Reβ(l â r ). For (ijyÏÎ, we ...
Bernard S. Institute for Theoretical ... Bernard S. Kay of gravity themselves can be ...... Abers, E. S., Lee, B. W. : Gauge Theories. Phys. Lett. 9C, 1-141 (1973). 38.
Sep 27, 1976 - $\left\{\begin{array}{l}dy(t)=\sigma(y(t), t)dB_{t}+g(y(t), ... standard process on $X$ by $M=\{\Omega, \mathcal{M}, \mathcal{M}_{t}, X_{t}, P_{x}, \theta_{t}, \zeta\}$ .... is considered as a function extended to $X_{\Delta}$.
MURAD BANAJI† AND GHEORGHE CRACIUN‡. Abstract. We extend previous
work on injectivity in chemical reaction networks to general interaction networks.
generalized Coleman theorem that in two space-time dimensions the vacuum is .... algebra of (quasi) local observables is stf â norm closure of (J £0(Î). A.
BY RONALD R. COIFMAN AND GUIDO WEISS1. Communicated by Elias Stein, June 22, 1973. The purpose of this note is to describe how central multiplier ...
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 80, Number 1, January 1974
CENTRAL MULTIPLIER THEOREMS FOR COMPACT LIE GROUPS BY RONALD R. COIFMAN AND GUIDO WEISS1 Communicated by Elias Stein, June 22, 1973
The purpose of this note is to describe how central multiplier theorems for compact Lie groups can be reduced to corresponding results on a maximal torus. We shall show that every multiplier theorem for multiple Fourier series gives rise to a corresponding theorem for such groups and, also, for expansions in terms of special functions. We use the notation and terminology of N. J. Weiss [4]. Let G denote a simply connected semisimple Lie group, g its Lie algebra and ï) a maximal abelian subalgebra; P+ the set of positive roots in I)*, the dual of t) (with respect to some order), and ( , ) is the inner product on f)* induced by the Killing form. With X=(Xl9 • • • , Xx) e Zl we associate the weight A=2l=i^" where TTÎ are the fundamental weights adapted to the simple roots. The characters %x of G are then indexed by those X with nonnegative integer coefficients. The degree dx of the corresponding representation is then given by
The symmetric trigonometric polynomials on ï)/Z* are defined by C A (T)= 2 et(X,tT{T)), where Wis the Weyl group. We can now state I. {mk} defines a bounded operator on LV(G), l
