Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spaces of dyadic distributions   In this paper subdivision schemes, which are used for functions approximation
and curves generation, are considered. In classical case, for the functions
defined on the real line, the theory of subdivision schemes is widely known due
to multiple applications in constructive approximation theory, signal
processing as well as for generating fractal curves and surfaces. Subdivision
schemes on a dyadic half-line, which is the positive half-line, equipped with
the standard Lebesgue measure and the digitwise binary addition operation,
where the Walsh functions play the role of exponents, are defined and studied.
Necessary and sufficient convergence conditions of the subdivision schemes in
terms of spectral properties of matrices and in terms of the smoothness of the
solution of the corresponding refinement equation are proved. The problem of
the convergence of subdivision schemes with non-negative coefficients is also
investigated. Explicit convergence criterion of the subdivision schemes with
four coefficients is obtained. As an auxiliary result fractal curves on a
dyadic half-line are defined and the formula of their smoothness is proved. The
paper contains various illustrations and numerical results.

36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph