application of this property, a theorem on analytic continuation of solutions of infinite ... The method used was a division theorem of certain entire functions by the ...
This extends a theorem of Gaier [6]. In Gaier's theorem, condition (1.6) is replaced by the hypothesis thatf has finite order p and mean type Talong a ray,.
Ap(V) = {a = {ak}kEN : 2A, B > 0, lakl. Aexp(Bp((k )), Vk ..... E = {a = {ak}kEN ~ Iakl exp(âMp((k)) < 1,k E N}. Then the space .... I, Wadsworth, Inc ., Califonia, 1990.
Functions. George Csordas. Department of Mathematics, University of Hawaii, Honolulu, HI 96822. E-mail: [email protected] ... Newman constant.
Jan 20, 2011 - x â¦â Ï (Pxl ) Al(E) ⤠Mk ÏAkâl(E)â². PAk(E). Proposition 3.9. Let {Bk (Eâ²)}kbe a coherent multiplicative sequence and {Ak(E)}k be such that ...
Jul 8, 2016 -
For a detailed investigation of the nuclear Fréchet spaces 7? satisfying 77(7?) = 77ub(7?) we refer to .... we get by the Cauchy inequalities that the polynomial.
ABSTRACT. We prove that for a nuclear locally convex complex vector space .... U in E and a Banach disk Bin G such that for every r > 0 the set f(rU) is bounded.
Feb 10, 2017 - Vgf(x, ξ) = â«Rdf(t) g(t â x) eâ2Ïiξt dt = ãf,Ï(z)gã z = (x, ξ), where the integral is intended as the (anti-)duality between Sâ² and S. The short-.
Nov 30, 2016 - Violator Spaces were introduced by J. Matoušek et al. in 2008 as ... that violator spaces with an unique basis satisfies the anti-exchange.
Aug 20, 2018 - ply connected open set D â C, and disjoint relatively compact subsets ..... choose CR to contain at least two points of maximum modulus of ...
Jeffrey C. Lagarias ... 2 H i lbe rt Spa c es o f E ntir e F unction s. We give a ...... L . de Branges, Hilbert Spaces of Entire Functions, Prentice-Hall:v nglewood. C liff ...
Dec 2, 2016 - In analogy to Beurling's sampling theorem for the Paley-Wiener ... theory of Gabor frames, we show that the set of phase-space shifts of g with.
Sep 6, 2012 - Let [am] be the median of the spherical triangle (possibly degenerate) △abc ⊂. S2, and d(a, b) + d(a, c) < π. Then d(a, m) ≤. 1. 2. (d(a, b) + d(a, ...
Aug 6, 2015 - Let E and F be separated convex bornological vector spaces, where ..... Let's move towards the proof of the Closed Graph Theorem, and before ...
Effective theorems for quadratic spaces over Q. Lenny Fukshansky. Texas A&M University. January 2006. 1. Page 2. Notation and heights. ⢠K is a number field ...
real number λ(U) to every open subset U of the semantic domain in such a way that ..... Scott topology of a domain admit extensions to Borel measures.
Jan 30, 2008 - EFFECTIVE STRUCTURE THEOREMS FOR SYMPLECTIC. SPACES VIA HEIGHT. LENNY FUKSHANSKY. Abstract. Given a 2k-dimensional ...
IN this paper we study the geometry of the space of Bochner integrable functions as ..... We also have for any A e si and any n-tuple of rationals (ru ⢠⢠â¢, rn). 1 '-1.
lsc convex function with a dense domain belongs to the class G1(X) if, and only if, ... Given a lsc convex function g and a lsc function f such that the domain of the.
Sandwich Theorems for Some Analytic Functions Defined by .... The operator Hl,s(α1), contains many interesting operators, such as Hohlov linear opera-.
Aug 28, 2012 - belongs to the domain of attraction of a stable law, (c) the tails of F belong to ... Key words and phrases: weighted renewal function, Blackwell ...
Key words: measure chains,time scale, Green's function ... To understand this so-called differential equation on a measure chain(time scale) we need some.
approach is to extend de Branges' basic theory of Hilbert spaces of entire func- ... 4/(X)|| and the evaluation functional {ez\ z E C'} on H where ez(f) = f(z) to-.
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 83, Number 4, July 1977
RESEARCH ANNOUNCEMENTS The purpose of this department is to provide early announcement of new results of such immediate importance to a substantial set of mathematicians that their communication to the mathematical community cannot await the normal time of publication. Research Announcements are communicated to the Bulletin by members of the Publications Committees listed on the inside back cover; manuscripts should be sent directly to any one of them. Each communicator is limited to accepting not more than six announcements each year; announcements are limited to 100 typed lines of 65 spaces each.
CLOSURE THEOREMS FOR SPACES OF ENTIRE FUNCTIONS BY LOREN D. PITT1 Communicated by Richard R. Goldberg, December 8, 1976
We announce a number of single variable approximation theorems. Our approach is to extend de Branges' basic theory of Hilbert spaces of entire functions [2] to a Banach space setting. The resulting structure is sufficiently rich to provide both new approximation results and a unifying structure for many earlier results on approximation by entire functions which are related to the Bernstein approximation problem, for example, Akutowitz [1], Koosis [3], Levinson and McKean [5], Mergelyan [6], Pitt [7] and Pollard [8]. Let Cc be the space of continuous complex functions m(X) on R1 with compact support and the supremum norm \m\. B denotes a fixed Banach function space on Rl with (semi) norm ||/||. We assume that (1) Cc n B is dense in B, and (2) The multiplication operator (m, ƒ ) —• m(K)f(K) is jointly continuous from Cc x B into B. Examples of spaces satisfying (1) and (2) are LP spaces, Orlicz spaces, Lorentz spaces L(p>q) and spaces of continuous functions with weighted supremum norms. Because of condition (2) it follows that for ƒ G B and e EB*, the linear functional on Cc given by m —• (mf, e) is expressible in the form 0 } then
for each z E R2 +.
2. Zétf ^ = {he H: h(p) = 0}. ƒƒ # ft symmetric and if 0? - X)- *#£ ö dense in H for some j3 with Im(/J) =£ 0 rte« H = 5 iffL+(fi) = + °°. THEOREM
3. If j}ER2 + and 0 < Z(j3) < rtercI(z) ft continuous and subharmonic on R2*. If in addition 0
