We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as quaternionic (QLCT). Using properties of LCT we establish an uncertainty principle for QLCT. This prescribes a lower bound on product effective widths signals in spatial and frequency domains. It is shown that only 2D Gaussian signal minimizes uncertainty.

Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space finite interval and the Paley–Wiener bandlimited on real line. No other system classical is known to obey this unique property. This raises question whether they these properties in Clifford analysis. The aim article answer extend results more flexible integral transforms, such as offset linear canonical transform. We also illustrate how use generalized...

In the present paper, we generalize linear canonical transform (LCT) to quaternion‐valued signals, known as quaternionic LCT (QLCT). Using properties of LCT, establish an uncertainty principle for two‐sided QLCT. This prescribes a lower bound on product effective widths signals in spatial and frequency domains. It is shown that only Gaussian signal minimizes uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.

Models of our universe lack consistency at different energy scales, so we require a theory with ultraviolet (UV) completion such as string theory. A suitable candidate to model in this framework is de Sitter space, spacetime which expands and has positive curvature. When describing the expansion however, one computes wrong sign for cosmological constant that would not allow an expanding universe. This motivates consider corrections from quantum reproduce correct constant. The conditions...

The main goal of this article is to generalize Hadamard's real part theorem and invariant forms Borel–Carathéodory's from complex analysis solutions the Riesz system in three-dimensional Euclidean space framework quaternionic analysis.

In recent years, much attention has been paid to the role of classical special functions a real or complex variable in mathematical physics, especially boundary value problems (BVPs). present paper, we propose higher‐dimensional analogue generalized Bessel polynomials within Clifford analysis via set monogenic polynomials. We give definition and derive number important properties (GMBPs), which are defined by generating exponential function shown satisfy an Rodrigues' formula. As...

The autonomous identification of animal births has a significant added value, since it enables for prompt timely human intervention in the process, protecting young and mothers’ health, without requiring continuous surveillance. Wearable inertial sensors have been employed variety monitoring applications, thanks to their low cost fact that they allow less invasive process. Alarms triggered by occurrence events must be generated close avoid delays caused communication latency, which is why...

The main goal of this paper is to construct Orthogonal Appell systems polynomial solutions the Riesz and Moisil-Théodoresco in finite cylinders ℝ3. This will be done spaces square integrable functions over ℝ ℍ. Some important properties are discussed. Copyright © 2011 John Wiley & Sons, Ltd.

The paper aims to study differential subordination and superordination preserving properties for certain analytic multivalent functions within the open unit disk related a novel generalized fractional derivative operator higher-order derivatives. As an application, we provide explicit construction complex potential (the velocity) stream function of two-dimensional fluid flow problems over circular cylinder using both vortex source/sink. We further determine produced by single source...

A function from a domain in to the quaternions is said be inframonogenic if , where . All functions are biharmonic. In context of taking values reduced quaternions, we show that homogeneous polynomials degree form subspace dimension We use construct an explicit, computable orthogonal basis for Hilbert space square‐integrable defined ball

We construct of a family fundamental solutions for elliptic partial differential operators with real constant coefficients. The elements such are expressed by means jointly analytic functions the coefficients and spatial variable. show regularity properties in frame Schauder spaces corresponding single layer potentials.

The windowed Fourier transform replaces the transform's sinusoidal wave by product of a sinusoid and window which is localized in time. It has been shown to represent powerful tool for non-stationary signals time-varying systems. In present paper, we investigate uncertainty principles short-time spectral domain. Two sharper complex are proposed. tighter lower bounds related covariance time frequency, can be achieved chirp with Gaussian envelope. results presented this paper explain...