Zobrazeno 1 - 10
of 195
pro vyhledávání: '"MASSOPUST, PETER"'
The novel concept of box spline of complex degree is introduced and several of its properties derived and discussed. These box splines of complex degree generalize and extend the classical box splines. Relations to a class of fractional derivatives d
Externí odkaz:
http://arxiv.org/abs/2309.02131
Autor:
Jahn, Marvin, Massopust, Peter
We introduce the novel concept of integral Read-Bajraktarevi\'c (iRB) operator and discuss some of its properties. We show that this iRB operator generalizes the known Read-Bajraktarevi\'c (RB) operator and we derive conditions for the fixed point of
Externí odkaz:
http://arxiv.org/abs/2308.00459
Autor:
Massopust, Peter R.
This paper introduces the novel concept of fractal interpolation over curves in Banach spaces. The contents are based on the usual methodologies involving the fractal interpolation problem over intervals but the current approach considerably extends
Externí odkaz:
http://arxiv.org/abs/2209.01033
Autor:
Massopust, Peter R.
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this c
Externí odkaz:
http://arxiv.org/abs/2203.07935
Autor:
Massopust, Peter R.
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential geometry and
Externí odkaz:
http://arxiv.org/abs/2112.04232
Autor:
Massopust, Peter R
We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references given to the
Externí odkaz:
http://arxiv.org/abs/2108.13685
In this paper, we introduce a class of $B$-splines on the Heisenberg group $\mathbb{H}$ and study their fundamental properties. Unlike the classical case, we prove that there does not exist any sequence $\{\alpha_n\}_{n\in\mathbb{N}}$ such that $L_{(
Externí odkaz:
http://arxiv.org/abs/2105.07707
Autor:
Massopust, Peter R
The existence of fundamental cardinal exponential B-splines of positive real order $\sigma$ is established subject to two conditions on $\sigma$ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-spl
Externí odkaz:
http://arxiv.org/abs/2009.10384
Autor:
Verma, S., Massopust, Peter R.
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on $[0,1]$ and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions are also in
Externí odkaz:
http://arxiv.org/abs/2002.05061