Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust’s theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent ...

This paper presents an on the spot methodology of reducing convolution processing time using hardware computing and implementations of discrete linear convolution of two finite length sequences (NXN). This implementation method is realized by simplifying the convolution building blocks. The purpose of this analysis is to prove the feasibility of an FPGA that performs a convolution on an acquire...

There is a well developed theory of saturation for positive convolution operators on C*, the space of 2n-periodic and continuous functions. Up until recently, this was suitable to handle almost all the important approximation processes on C*. Now, however, some new and interesting sequences of operators have been obtained for C* by discretizing convolution operators [1], [5]. Such a discretized...

It is well known that the topography in atomic force microscopy (AFM) is a convolution of the tip's shape and the sample's geometry. The classical convolution model was established in contact mode assuming a static probe, but it is no longer valid in dynamic mode AFM. It is still not well understood whether or how the vibration of the probe in dynamic mode affects the convolution. Such ignoranc...

*Correspondence: [email protected] 2Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), Serdang, Selangor 43400, Malaysia Full list of author information is available at the end of the article Abstract In this paper, we extend Hartley and Hartley-Hilbert transformations (HT and HHT, respectively) to a certain space of tempered distribution...