Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Massopust, P. R."'
A novel approach to zipper fractal interpolation theory for functions of several variables is proposed. We develop multivariate zipper fractal functions in a constructive manner. We then perturb a multivariate function to construct its zipper $\alpha
Externí odkaz:
http://arxiv.org/abs/2211.08931
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-K\"onig-Zeller operator $M_{q,n}$. These quantum Meyer-K\"onig-Zeller (MKZ) fractal functions employ $M_{q,n} f$ as the base function in the iterated function
Externí odkaz:
http://arxiv.org/abs/2210.11163
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
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