Now showing items 41-60 of 62
The Gaussian cotype of operators from C(K)
We show that the canonical embedding C(K) to LΦ(μ) has Gaussian cotype p, where μ is a Radon probability measure on K, and Φ is an Orlicz function equivalent to tp(log t)p/2 for large t.
Shifts in the Spatio-Temporal Growth Dynamics of Shortleaf Pine
(Environmental and Ecological Statistics, 2007)
Previous studies focusing on the growth history of pinus echinata at the edge of its geographical range have suggested that changes in growth correspond to climatic and non-climatic (e.g., anthropogenic) factors. We employ ...
Decomposition of analytic measures on groups and measure spaces
This paper provides a new approach to proving generalizations of the F.&M. Riesz Theorem, for example, the result of Helson and Lowdenslager, the result of Forelli (and de Leeuw and Glicksberg), and more recent results of ...
Hardy martingales and Jensen's inequality
Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus TN, where analyticity is defined using a lexicographic order on the dual group ZN. We show how, by using basic ...
Multiplicative Structure of Values of the Euler Function
We establish upper bounds for the number of smooth values of the Euler function. In particular, although the Euler function has a certain “smoothing” effect on its integer arguments, our results show that, in fact, most ...
Congruences and Exponential Sums with the Euler Function
We give upper bounds for the number of solutions to congruences with the Euler function φ(n) and with the Carmichael function λ(n). We also give nontrivial bounds for certain exponential sums involving φ(n). Analogous ...
Squares from products of integers
Notice that 1_2_3_4+1 = 52 , 2_3_4_5+1 = 112 , 3_4_5_6+1 = 192 , . . . . Indeed, it is well known that the product of any four consecutive integers always differs by one from a perfect square. However, a little experimentation ...
Boyd indices of Orlicz-Lorentz spaces
Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska-Orlicz indices of the ...
Vector-valued weakly analytic measures
This paper studies properties of weakly analytic vector-valued measures, an area of study which is relatively unexplored, especially in comparison with scalar-valued measures.
A Kernel-Based Spectral Model for Non-Gaussian Spatio-Temporal Processes
(Statistical Modelling, 2002)
Spatio-temporal processes can often be written as hierarchical state-space processes. In situations with complicated dynamics such as wave propagation, it is difficult to parameterize state transition functions for ...
Multiresolution Models for Nonstationary Spatial Covariance Functions
(Statistical Modelling, 2002)
Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of a multiresolution ...
New examples of noncommutative Λ(p) sets
In this paper, we introduce a certain combinatorial property Z*(k), which is defined for every integer k ≥ 2, and show that every set E ⊂ Z with the property Z*(k) is necessarily a noncommutative Λ (2k) set. In particular, ...
Almost All Palindromes Are Composite
We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x as x → ∞. Our results ...
Irrationality of Power Series for Various Number Theoretic Functions
We study formal power series whose coefficients are taken to be a variety of number theoretic functions, such as the Euler, Möbius and divisor functions. We show that these power series are irrational over ℤ [X], and we ...
On the Value Set of n! Modulo a Prime
We show that for infinitely many prime numbers p there are at least log log p/ log log log p distinct residue classes modulo p that are not congruent to n! for any integer n.
On the average value of divisor sums in arithmetic progressions
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that "on average" these sums are close to the expected value. We also give applications of our result to sums ...
Measuring the magnitude of sums of independent random variables
This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Lévy property. We then give ...
Concrete representation of martingales
Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0,1]n such that ∫01 dn(x1,...,xn) dxn = 0 for almost all x1,...,xn-1, and such that the law of (fn) is the same ...
A transference theorem for ergodic H1
In this paper, we extend the basic transference theorem for convolution operators on Lp spaces of Coifman and Weiss to H1 spaces.
Evolutionary semigroups and Lyapunov theorems in Banach spaces
We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from ...