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Inequalities in the Setting of Clifford Analysis
In this paper, we prove the Riemann-Lebesgue lemma for the Clifford-Fourier transform. We give an alternative proof of Heisenberg’s inequality....
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Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set
This article focuses on the dynamics of the different tridimensional principal slices of the multicomplex Multibrot sets. First, we define an...
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Structural Results for Quaternionic Gabor Frames
We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not...
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The Octonionic Bergman Kernel for the Unit Ball
By introducing a suitable new definition for the inner product of the octonionic Bergman space on the unit ball, we determine the explicit form of...
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Quasi-monogenic Functions
The aim of this work is to introduce quasi-monogenic functions, to prove their properties and to discuss some examples. Quasi-monogenic functions are...
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On a Dirichlet Problem for a Generalized Beltrami Equation
In this article we study a Dirichlet problem for a hypercomplex Beltrami equation. We prove the existence of a unique solution of the problem and...
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First and Second Fundamental Solutions of the Time-Fractional Telegraph Equation with Laplace or Dirac Operators
In this work we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac...
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Eigen-Decomposition of Quaternions
This paper introduces biquaternion eigen-decomposition theory (via Peirce decomposition) with respect to a selected quaternion with a non-zero vector...
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Special Classes of Monogenic Functions in \(\mathbb {H}\)
Recently, the classical orthogonal function systems of inner and outer monogenic Appell functions were used to find a new class of monogenic...
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Modified Spherical Harmonics in Four Dimensions
The classical theory of spherical harmonics on the unit sphere S is well-known. In an earlier paper, entitled “Modified Spherical Harmonics”, we...
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Gleason’s Problem Associated to a Real Ternary Algebra and Applications
This paper is an introduction of a new class of analytic functions defined on a ternary algebra, a three dimensional structure different from
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On a Class of Monogenic Functions with (Logarithmic) Line Singularities
In the article a new class of monogenic functions with (logarithmic) line singularities is studied, which naturally extend the classical system of...
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Uncertainty Principles for the Clifford–Fourier Transform
In this paper, we establish analogues of Hardy’s and Miyachi’s theorems for the Clifford–Fourier transform.
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On k-Analytic Functions of an Octonionic Variable
A theory of k -analytic functions on octonions is established. The Cauchy integral formulas, Taylor series and Laurent series for the k -analytic...
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Bicomplex Harmonic and Isotonic Oscillators: The Excited States
We investigate the complete analytical solutions of quantum mechanical harmonic and isotonic oscillators formulated in the commutative ring of...
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Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets
In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal...
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General Solution of the Inhomogeneous Div-Curl System and Consequences
We consider the inhomogeneous div-curl system (i.e. to find a vector field with prescribed div and curl) in a bounded star-shaped domain in
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