26 citations · 59 across the 28 of their papers we have counts for
23 papers · 1 filter
An Integral RB Operator
Marvin Jahn, Peter Massopust
We introduce the novel concept of integral Read-Bajraktarević (iRB) operator and discuss some of its properties. We show that this iRB operator generalizes the known Read-Bajraktar…
Multivariate Zipper Fractal Functions
D. Kumar, A. K. B. Chand, P. R. Massopust
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. W…
Approximation by Quantum Meyer König and Zeller-Fractal Functions
D. Kumar, A. K. B. Chand, P. R. Massopust
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-König-Zeller operator . These quantum Meyer-König-Zeller (MKZ) fractal functions…
Fractal Interpolation over Curves
Peter R. Massopust
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…
Clifford-Valued Fractal Interpolation
Peter R. Massopust
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 mode…
Fractal Interpolation: From Global to Local, to Nonstationary and Quaternionic
Peter R Massopust
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. Emph…
B-splines on the Heisenberg group
Santi R. Das, Peter R. Massopust, Radha Ramakrishnan
In this paper, we introduce a class of -splines on the Heisenberg group and study their fundamental properties. Unlike the classical case, we prove that there does…
Interpolation and Sampling with Exponential Splines of Real Order
Peter R Massopust
The existence of fundamental cardinal exponential B-splines of positive real order is established subject to two conditions on and their construction is implemented. A samp…
Twisted B-splines in the complex plane
S. R. Das, P. Massopust, R. Radha
In this paper, we introduce the new class of twisted -splines and study some properties of these B-splines. We also investigate the system of twisted translates and the wavelets…
Local average sampling and reconstruction with fundamental splines of fractional order
P. Devaraj, P. Massopust, S. Yugesh
We analyse sampling and average sampling techniques for fractional spline subspaces of Fractional B-splines are extensions of Schoenberg's polynomial s…
Attractors of Trees of Maps and of Sequences of Maps between Spaces with Application to Subdivision
Nira Dyn, David Levin, Peter Massopust
In a previous paper we considered a sequence of maps on a complete metric space and derived an extension of the Banach fixed point theorem. We showed that backward trajecto…
Splines and Fractional Differential Operators
Peter Massopust
Several classes of classical cardinal B-splines can be obtained as solutions of operator equations of the form where is a linear differential operator of integral orde…
Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling
Jeffrey A. Hogan, Peter R. Massopust
B-splines , $\Sc q > 1$, of quaternionic order , for short quaternionic B-splines, are quaternion-valued piecewise Müntz polynomials whose scalar parts interpolate the cl…
Quaternionic B-Splines
Jeffrey A. Hogan, Peter Massopust
We introduce B-splines on the line of quaternionic order ( in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions …
Fractional Cone Splines and Hex Splines
Peter R. Massopust, Patrick J. Van Fleet
We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certa…
Local fractal functions in Besov and Triebel-Lizorkin spaces
Peter Massopust
Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functio…
Directional time frequency analysis via continuous frame
Ole Christensen, Brigitte Forster, Peter Massopust
Grafakos and Sansing \cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L^2(\mr^n)$ based on Gabor systems in $\ltr;$ the key tool is the…
Exponential Splines of Complex Order
Peter Massopust
We extend the concept of exponential B-spline to complex orders. This extension contains as special cases the class of exponential splines and also the class of polynomial B-spline…
Local fractal functions and function spaces
Peter Massopust
We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal fu…
Fractal Hypersurfaces, Wavelet Sets and Affine Weyl Groups
Peter Massopust
In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal fu…
Fractional Operators, Dirichlet Averages, and Splines
Peter Massopust
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questi…
Coxeter Groups and Wavelet Sets
David Larson, Peter Massopust
A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of transl…
Three-way tiling sets in two dimensions
David Larson, Peter Massopust, Gestur Olafsson
In this article we show that there exist measurable sets W in the plane with finite measure that tile the plane in a measurable way under the action of a expansive matrix A, an aff…