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Relevant bibliographies by topics / Quaternionic function theory

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Journal articles

Academic literature on the topic 'Quaternionic function theory'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Quaternionic function theory"

1

Kim, Ji, and Kwang Shon. "Expansion of implicit mapping theory to split-quaternionic maps in Clifford analysis." Filomat 35, no. 11 (2021): 3833–40. http://dx.doi.org/10.2298/fil2111833k.

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This paper presents the regularity of a split-quaternionic function and a corresponding split- Cauchy-Riemann system of a split quaternion. The properties of an inverse and an implicit mapping theory for a split-quaternionic map are investigated. In addition, the paper proposes a definition and expression for a split biregular mapping in an open set in C2. The obtained results are illustrated with some examples.

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2

Pap, Margit, and Ferenc Schipp. "Quaternionic Blaschke Group." Mathematics 7, no. 1 (2018): 33. http://dx.doi.org/10.3390/math7010033.

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In the complex case, the Blaschke group was introduced and studied. It turned out that in the complex case this group plays important role in the construction of analytic wavelets and multiresolution analysis in different analytic function spaces. The extension of the wavelet theory to quaternion variable function spaces would be very beneficial in the solution of many problems in physics. A first step in this direction is to give the quaternionic analogue of the Blaschke group. In this paper we introduce the quaternionic Blaschke group and we study the properties of this group and its subgrou

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3

Gentili, Graziano, and Caterina Stoppato. "Geometric function theory over quaternionic slice domains." Journal of Mathematical Analysis and Applications 495, no. 2 (2021): 124780. http://dx.doi.org/10.1016/j.jmaa.2020.124780.

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4

Morais, J., and M. A. Pérez-de la Rosa. "Towards a quaternionic function theory linked with the Lamé's wave functions." Mathematical Methods in the Applied Sciences 38, no. 17 (2015): 4365–87. http://dx.doi.org/10.1002/mma.3376.

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5

Alpay, Daniel, Fabrizio Colombo, and Irene Sabadini. "Perturbation of the generator of a quaternionic evolution operator." Analysis and Applications 13, no. 04 (2015): 347–70. http://dx.doi.org/10.1142/s0219530514500249.

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The theory of slice hyperholomorphic functions, introduced in recent years, has important applications in operator theory. The quaternionic version of this function theory and its Cauchy formula yield to a definition of the quaternionic version of the Riesz–Dunford functional calculus which is based on the notion of S-spectrum. This quaternionic functional calculus allows to define the quaternionic evolution operator which appears in the quaternionic version of quantum mechanics proposed by J. von Neumann and later developed by S. L. Adler. Generation results such as the Hille–Phillips–Yosida

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6

Konno, Norio, Kaname Matsue, Hideo Mitsuhashi, and Iwao Sato. "Quaternionic quantum walks of Szegedy type and zeta functions of graphs." Quantum Information and Computation 17, no. 15&16 (2017): 1349–71. http://dx.doi.org/10.26421/qic17.15-16-6.

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We define a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk on a graph to be quaternionic unitary is given. In order to derive the spectral mapping theorem for the quaternionic Szegedy walk, we derive a quaternionic extension of the determinant expression of the second weighted zeta function of a graph. Our main results determine explicitly all the right eigenvalues of the quaternionic Szegedy walk by using complex right eigenvalues of the corresponding doubly weighted matrix

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7

Abreu Blaya, Ricardo, Juan Bory Reyes, Alí Guzmán Adán та Uwe Kaehler. "On some structural sets and a quaternionic (φ,ψ)-hyperholomorphic function theory". Mathematische Nachrichten 288, № 13 (2015): 1451–75. http://dx.doi.org/10.1002/mana.201300072.

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8

Shpakivskyi, V. S., and T. S. Kuzmenko. "Integral theorems for the quaternionic G-monogenic mappings." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (2016): 271–81. http://dx.doi.org/10.1515/auom-2016-0042.

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Abstract In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for G-monogenic mappings.

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9

Shapiro, M. V., та N. L. Vasilevski. "Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems I. ψ-hyperholomorphic function theory". Complex Variables, Theory and Application: An International Journal 27, № 1 (1995): 17–46. http://dx.doi.org/10.1080/17476939508814803.

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10

Kravchenko, V. V., and M. V. Shapiro. "Helmholtz operator with a quaternionic wave number and associated function theory. II. Integral representations." Acta Applicandae Mathematicae 32, no. 3 (1993): 243–65. http://dx.doi.org/10.1007/bf01082451.

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