Related papers: On the Clifford-Fourier transform
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…
Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
The Howe dual pair (sl(2),O(m)) allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen element of sl(2) such that the Helmholtz relations are…
We define an integral form of shifted quantum affine algebras of type $A$ and construct Poincar\'e-Birkhoff-Witt-Drinfeld bases for them. When the shift is trivial, our integral form coincides with the RTT integral form. We prove that these…
We present an Almansi-type decomposition for polynomials with Clifford coefficients, and more generally for slice-regular functions on Clifford algebras. The classical result by Emilio Almansi, published in 1899, dealt with polyharmonic…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on the quantum SU(1,1) group is studied,…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
We deduce from a determinant identity on quantum transfer matrices of generalized quantum integrable spin chain model their generating functions. We construct the isomorphism of Clifford algebra modules of sequences of transfer matrices and…
We show how for $n=2,3 (\mod 4)$ continuous Clifford (geometric) algebra (GA) $Cl_n$-valued admissible wavelets can be constructed using the similitude group $SIM(n)$. We strictly aim for real geometric interpretation, and replace the…
We provide a generalized definition for the quantized Clifford algebra introduced by Hayashi using another parameter $k$ that we call the twist. For a field of characteristic not equal to $2$, we provide a basis for our quantized Clifford…
We extend the functional analytic approach to Colombeau-type spaces of nonlinear generalized functions in order to study algebras of tempered generalized functions. We obtain a definition of Fourier transform of nonlinear generalized…
Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on $m$-dimensional euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford algebra…
The Riesz transform of $u$ : $\mathcal{S}(\mathbb{R}^n) \rightarrow \mathcal{S'}(\mathbb{R}^n)$ is defined as a convolution by a singular kernel, and can be conveniently expressed using the Fourier Transform and a simple multiplier. We…
We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored…
In this paper, we study a specific system of Clifford-Appell polynomials and in particular their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions.…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…