scholarly journals Oscillation of uniformly continuous functions on unit spheres of finite-dimensional subspaces

1999 ◽  
pp. 281-300
Keyword(s):  
Continuous Functions ◽  
Finite Dimensional ◽  
Uniformly Continuous

scholarly journals Convergence of Locally Square Integrable Martingales to a Continuous Local Martingale

2011 ◽  
Vol 2011 ◽  
pp. 1-34
Author(s):  
Andriy Yurachkivsky
Keyword(s):  
Gaussian Processes ◽  
Continuous Functions ◽  
Local Martingale ◽  
Initial Value ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Integrable Martingale ◽  
Probability Spaces ◽  
Uniformly Continuous

Let for each be an -valued locally square integrable martingale w.r.t. a filtration (probability spaces may be different for different ). It is assumed that the discontinuities of are in a sense asymptotically small as and the relation holds for all , row vectors , and bounded uniformly continuous functions . Under these two principal assumptions and a number of technical ones, it is proved that the 's are asymptotically conditionally Gaussian processes with conditionally independent increments. If, moreover, the compound processes converge in distribution to some , then a sequence () converges in distribution to a continuous local martingale with initial value and quadratic characteristic , whose finite-dimensional distributions are explicitly expressed via those of .

scholarly journals Lattices of uniformly continuous functions

2013 ◽  
Vol 160 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Félix Cabello Sánchez ◽  
Javier Cabello Sánchez
Keyword(s):  
Continuous Functions ◽  
Uniformly Continuous

Higher Dimensional Spaces of Functions on the Spectrum of a Uniform Algebra

2007 ◽  
Vol 50 (1) ◽  
pp. 3-10
Author(s):  
Richard F. Basener
Keyword(s):  
Continuous Functions ◽  
Uniform Algebra ◽  
Finite Dimensional ◽  
Higher Dimensional ◽  
Spaces Of Continuous Functions ◽  
The Family ◽  
Continuous Complex ◽  
Finite Dimensional Case ◽  
Complex Valued ◽  
Shed Light

AbstractIn this paper we introduce a nested family of spaces of continuous functions defined on the spectrum of a uniform algebra. The smallest space in the family is the uniform algebra itself. In the “finite dimensional” case, from some point on the spaces will be the space of all continuous complex-valued functions on the spectrum. These spaces are defined in terms of solutions to the nonlinear Cauchy–Riemann equations as introduced by the author in 1976, so they are not generally linear spaces of functions. However, these spaces do shed light on the higher dimensional properties of a uniform algebra. In particular, these spaces are directly related to the generalized Shilov boundary of the uniform algebra (as defined by the author and, independently, by Sibony in the early 1970s).

scholarly journals Remarks on uniformly symmetrically continuous functions

2016 ◽  
Vol 09 (03) ◽  
pp. 1650069
Author(s):  
Tammatada Khemaratchatakumthorn ◽  
Prapanpong Pongsriiam
Keyword(s):  
Real Line ◽  
Nonempty Subset ◽  
Continuous Functions ◽  
The Real ◽  
Definition Of ◽  
Symmetrically Continuous Functions ◽  
Uniformly Continuous

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.

Sign in / Sign up

Export Citation Format

Share Document