منابع مشابه
Irregularities of Distribution, Ii
(1.2) \D[zu ..., zn ; B(x, r)]\ > c2(K, e). n < Note that the exponent {\ — (1/2K) e) of n is essentially the best possible: (2 — (1/2K) e) cannot be replaced by the exponent (2 — (1/2K) + e) with e > 0. Note further that (1.1) or (1.2) above guarantees the existence of a ball in U with 'error' very large as compared to that of boxes in U with sides parallel to the axes. We recall that in 1954 ...
متن کاملNote on Irregularities of Distribution Ii
THEOREM IB (Roth [11]). For every natural number N^2, there exists a distribution 0* of N points in U such that I. L-l \DL[&;B(y)]\dy«L(\ogN) u Note that Theorems 1A and IB remain true in the trivial case L = 1. Suppose now that ^ is a distribution of N points in the unit torus U = [0, 1)*, where K 5= 2. Let A be a compact and convex body in U. For any real number A € (0, 1], any proper orthogo...
متن کاملOn Irregularities of Distribution Iii
Dedicated to the memory of Gerold Wagner Abstract We study the L w -norm (2 < W < oo) of the discrepancy of a sequence of points in the unit cube relative to similar copies of a given convex polygon. In particular, we prove the rather surprising result that the estimates obtained have the same order of magnitude as the analogous question when the sequence of points is replaced by a set of point...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1969-0234923-0