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Journal articles on the topic 'Slice Regular Functions'

Author: Grafiati

Published: 10 March 2023

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1

Altavilla, A., and C. de Fabritiis. "$*$-exponential of slice-regular functions." Proceedings of the American Mathematical Society 147, no. 3 (December 6, 2018): 1173–88. http://dx.doi.org/10.1090/proc/14307.

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2

Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "Sheaves of slice regular functions." Mathematische Nachrichten 285, no. 8-9 (January 18, 2012): 949–58. http://dx.doi.org/10.1002/mana.201000149.

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3

Stoppato, Caterina. "Singularities of slice regular functions." Mathematische Nachrichten 285, no. 10 (February 21, 2012): 1274–93. http://dx.doi.org/10.1002/mana.201100082.

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4

Zhenghua, Xu, and Wang Ermin. "Proper slice regular functions over quaternions." SCIENTIA SINICA Mathematica 51, no. 12 (July 16, 2020): 1975. http://dx.doi.org/10.1360/scm-2018-0858.

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5

Altavilla, Amedeo. "Twistor interpretation of slice regular functions." Journal of Geometry and Physics 123 (January 2018): 184–208. http://dx.doi.org/10.1016/j.geomphys.2017.09.007.

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6

Ren, Guangbin, and Xieping Wang. "Carathéodory Theorems for Slice Regular Functions." Complex Analysis and Operator Theory 9, no. 5 (December 2, 2014): 1229–43. http://dx.doi.org/10.1007/s11785-014-0432-9.

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7

Ren, Guangbin, and Xieping Wang. "Julia theory for slice regular functions." Transactions of the American Mathematical Society 369, no. 2 (March 18, 2016): 861–85. http://dx.doi.org/10.1090/tran/6717.

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8

de Fabritiis, Chiara. "Transcendental operators acting on slice regular functions." Concrete Operators 9, no. 1 (January 1, 2022): 6–18. http://dx.doi.org/10.1515/conop-2022-0002.

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Abstract The aim of this paper is to carry out an analysis of five trascendental operators acting on the space of slice regular functions, namely *-exponential, *-sine and *-cosine and their hyperbolic analogues. The first three of them were introduced by Colombo, Sabadini and Struppa and some features of *-exponential were investigated in a previous paper by Altavilla and the author. We show how exp*(f ), sin*(f ), cos*(f ), sinh*(f ) and cosh*(f ) can be written in terms of the real and the vector part of the function f and we examine the relation between cos* and cosh* when the domain Ω is product and when it is slice. In particular we prove that when Ω is slice, then cos*(f ) = cosh*(f * I) holds if and only if f is ℂ I preserving, while in the case Ω is product there is a much larger family of slice regular functions for which the above relation holds.

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9

Dou, Xinyuan, Guangbin Ren, Irene Sabadini, and Ting Yang. "Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions." Journal of Geometric Analysis 31, no. 11 (May 12, 2021): 11312–37. http://dx.doi.org/10.1007/s12220-021-00682-5.

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AbstractIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.

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10

Ghiloni, R., and A. Perotti. "Slice regular functions on real alternative algebras." Advances in Mathematics 226, no. 2 (January 2011): 1662–91. http://dx.doi.org/10.1016/j.aim.2010.08.015.

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11

Ren, Guangbin, and Ting Yang. "Slice regular functions of several octonionic variables." Mathematical Methods in the Applied Sciences 43, no. 9 (March 17, 2020): 6031–42. http://dx.doi.org/10.1002/mma.6344.

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12

Rocchetta, Chiara Della, Graziano Gentili, and Giulia Sarfatti. "The Bohr Theorem for slice regular functions." Mathematische Nachrichten 285, no. 17-18 (July 23, 2012): 2093–105. http://dx.doi.org/10.1002/mana.201100232.

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13

Ghiloni, Riccardo, and Alessandro Perotti. "Global differential equations for slice regular functions." Mathematische Nachrichten 287, no. 5-6 (October 8, 2013): 561–73. http://dx.doi.org/10.1002/mana.201200318.

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14

Colombo, Fabrizio, Graziano Gentili, and Irene Sabadini. "A Cauchy kernel for slice regular functions." Annals of Global Analysis and Geometry 37, no. 4 (December 19, 2009): 361–78. http://dx.doi.org/10.1007/s10455-009-9191-7.

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15

Gentili, Graziano, Caterina Stoppato, and Daniele C. Struppa. "A Phragmén - Lindelöf principle for slice regular functions." Bulletin of the Belgian Mathematical Society - Simon Stevin 18, no. 4 (November 2011): 749–59. http://dx.doi.org/10.36045/bbms/1320763135.

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16

Han, Gang. "Quaternionic Slice Regular Functions and Quaternionic Laplace Transforms." Acta Mathematica Scientia 43, no. 1 (October 18, 2022): 289–302. http://dx.doi.org/10.1007/s10473-023-0116-5.

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17

Oscar González-Cervantes, J., and Irene Sabadini. "On some splitting properties of slice regular functions." Complex Variables and Elliptic Equations 62, no. 9 (March 2017): 1393–409. http://dx.doi.org/10.1080/17476933.2016.1250935.

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18

Vlacci, Fabio. "The argument principle for quaternionic slice regular functions." Michigan Mathematical Journal 60, no. 1 (April 2011): 67–77. http://dx.doi.org/10.1307/mmj/1301586304.

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19

Bisi, Cinzia, and Caterina Stoppato. "The Schwarz-Pick lemma for slice regular functions." Indiana University Mathematics Journal 61, no. 1 (2012): 297–317. http://dx.doi.org/10.1512/iumj.2012.61.5076.

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20

Stoppato, Caterina. "A new series expansion for slice regular functions." Advances in Mathematics 231, no. 3-4 (October 2012): 1401–16. http://dx.doi.org/10.1016/j.aim.2012.05.023.

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21

Altavilla, A., and C. de Fabritiis. "s-Regular functions which preserve a complex slice." Annali di Matematica Pura ed Applicata (1923 -) 197, no. 4 (January 29, 2018): 1269–94. http://dx.doi.org/10.1007/s10231-018-0724-1.

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22

Bisi, Cinzia, and Caterina Stoppato. "Landau’s theorem for slice regular functions on the quaternionic unit ball." International Journal of Mathematics 28, no. 03 (March 2017): 1750017. http://dx.doi.org/10.1142/s0129167x17500173.

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During the development of the theory of slice regular functions over the real algebra of quaternions [Formula: see text] in the last decade, some natural questions arose about slice regular functions on the open unit ball [Formula: see text] in [Formula: see text]. This work establishes several new results in this context. Along with some useful estimates for slice regular self-maps of [Formula: see text] fixing the origin, it establishes two variants of the quaternionic Schwarz–Pick lemma, specialized to maps [Formula: see text] that are not injective. These results allow a full generalization to quaternions of two theorems proven by Landau for holomorphic self-maps [Formula: see text] of the complex unit disk with [Formula: see text]. Landau had computed, in terms of [Formula: see text], a radius [Formula: see text] such that [Formula: see text] is injective at least in the disk [Formula: see text] and such that the inclusion [Formula: see text] holds. The analogous result proven here for slice regular functions [Formula: see text] allows a new approach to the study of Bloch–Landau-type properties of slice regular functions [Formula: see text].

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23

Ghiloni, Riccardo, Alessandro Perotti, and Caterina Stoppato. "Division algebras of slice functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 4 (March 15, 2019): 2055–82. http://dx.doi.org/10.1017/prm.2019.13.

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AbstractThis work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the Casorati-Weierstrass theorem.

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24

Altavilla, Amedeo. "On the real differential of a slice regular function." Advances in Geometry 18, no. 1 (January 26, 2018): 5–26. http://dx.doi.org/10.1515/advgeom-2017-0044.

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AbstractIn this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato and it is obtained thanks, in particular, to some new information regarding the first coefficients of a certain polynomial expansion for slice regular functions (calledspherical expansion), and to a new general result which says that the slice derivative of any injective slice regular function is different from zero. A useful tool proven in this paper is a new formula that relates slice and spherical derivatives of a slice regular function. Given a slice regular function, part of its singular set is described as the union of surfaces on which it results to be constant.

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25

Sarfatti, Giulia. "Quaternionic Hankel operators and approximation by slice regular functions." Indiana University Mathematics Journal 65, no. 5 (2016): 1735–57. http://dx.doi.org/10.1512/iumj.2016.65.5896.

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26

REN, GuangBin, ZhengHua XU, and XiePing WANG. "Recent development of the theory of Slice regular functions." SCIENTIA SINICA Mathematica 45, no. 11 (November 1, 2015): 1779–90. http://dx.doi.org/10.1360/n012015-00151.

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27

Altavilla, A., and C. de Fabritiis. "Equivalence of slice semi-regular functions via Sylvester operators." Linear Algebra and its Applications 607 (December 2020): 151–89. http://dx.doi.org/10.1016/j.laa.2020.08.009.

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28

Cervantes, J. Oscar González. "On Cauchy Integral Theorem for Quaternionic Slice Regular Functions." Complex Analysis and Operator Theory 13, no. 6 (March 14, 2019): 2527–39. http://dx.doi.org/10.1007/s11785-019-00913-2.

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29

Ghiloni, Riccardo, Alessandro Perotti, and Caterina Stoppato. "Singularities of slice regular functions over real alternative ⁎-algebras." Advances in Mathematics 305 (January 2017): 1085–130. http://dx.doi.org/10.1016/j.aim.2016.10.009.

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30

Gentili, Graziano, and Giulia Sarfatti. "Landau–Toeplitz theorems for slice regular functions over quaternions." Pacific Journal of Mathematics 265, no. 2 (August 28, 2013): 381–404. http://dx.doi.org/10.2140/pjm.2013.265.381.

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31

Kumar, Sanjay, S. D. Sharma, and Khalid Manzoor. "Quaternionic Fock space on slice hyperholomorphic functions." Filomat 34, no. 4 (2020): 1197–207. http://dx.doi.org/10.2298/fil2004197k.

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In this paper, we define the quaternionic Fock spaces F p? of entire slice hyperholomorphic functions in a quaternionic unit ball B in H: We also study growth estimates and various results of entire slice regular functions in these spaces. The work of this paper is motivated by the recent work of [5] and [26].

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32

Kumar, Sanjay, S. D. Sharma, and Khalid Manzoor. "Quaternionic Fock space on slice hyperholomorphic functions." Filomat 34, no. 4 (2020): 1197–207. http://dx.doi.org/10.2298/fil2004197k.

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In this paper, we define the quaternionic Fock spaces F p? of entire slice hyperholomorphic functions in a quaternionic unit ball B in H: We also study growth estimates and various results of entire slice regular functions in these spaces. The work of this paper is motivated by the recent work of [5] and [26].

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33

Gori, Anna, and Fabio Vlacci. "On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions." Proceedings of the Edinburgh Mathematical Society 62, no. 1 (August 28, 2018): 97–105. http://dx.doi.org/10.1017/s0013091518000226.

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AbstractA new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical interpretation for analytic conditions on the real Jacobian associated with a slice regular function f. The criterion involves spherical and Cullen derivatives of f and gives rise to several geometric implications, including an application to related conformality properties.

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34

Gal, Sorin G., J. Oscar González-Cervantes, and Irene Sabadini. "Univalence results for slice regular functions of a quaternion variable." Complex Variables and Elliptic Equations 60, no. 10 (March 16, 2015): 1346–65. http://dx.doi.org/10.1080/17476933.2015.1015530.

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35

Wang, Xieping. "On Geometric Aspects of Quaternionic and Octonionic Slice Regular Functions." Journal of Geometric Analysis 27, no. 4 (February 16, 2017): 2817–71. http://dx.doi.org/10.1007/s12220-017-9784-5.

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36

Colombo, Fabrizio, Graziano Gentili, Irene Sabadini, and Daniele Struppa. "Extension results for slice regular functions of a quaternionic variable." Advances in Mathematics 222, no. 5 (December 2009): 1793–808. http://dx.doi.org/10.1016/j.aim.2009.06.015.

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37

Liang, Yuxia. "The Product Operator between Bloch-Type Spaces of Slice Regular Functions." Acta Mathematica Scientia 41, no. 5 (June 29, 2021): 1606–18. http://dx.doi.org/10.1007/s10473-021-0512-7.

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38

Gentili, Graziano, and Irene Vignozzi. "The Weierstrass factorization theorem for slice regular functions over the quaternions." Annals of Global Analysis and Geometry 40, no. 4 (May 4, 2011): 435–66. http://dx.doi.org/10.1007/s10455-011-9266-0.

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39

Altavilla, Amedeo. "Some properties for quaternionic slice regular functions on domains without real points." Complex Variables and Elliptic Equations 60, no. 1 (February 25, 2014): 59–77. http://dx.doi.org/10.1080/17476933.2014.889691.

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40

Gal, Sorin G., J. Oscar González-Cervantes, and Irene Sabadini. "On some geometric properties of slice regular functions of a quaternion variable." Complex Variables and Elliptic Equations 60, no. 10 (March 30, 2015): 1431–55. http://dx.doi.org/10.1080/17476933.2015.1024670.

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41

Amedeo, Altavilla, and Chiara de Fabritiis. "Applications of the Sylvester operator in the space of slice semi-regular functions." Concrete Operators 7, no. 1 (February 4, 2020): 1–12. http://dx.doi.org/10.1515/conop-2020-0001.

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AbstractIn this paper we apply the results obtained in [3] to establish some outcomes of the study of the behaviour of a class of linear operators, which include the Sylvester ones, acting on slice semi-regular functions. We first present a detailed study of the kernel of the linear operator ℒf,g (when not trivial), showing that it has dimension 2 if exactly one between f and g is a zero divisor, and it has dimension 3 if both f and g are zero divisors. Afterwards, we deepen the analysis of the behaviour of the -product, giving a complete classification of the cases when the functions fv, gv and fvgv are linearly dependent and obtaining, as a by-product, a necessary and sufficient condition on the functions f and g in order their *-product is slice-preserving. At last, we give an Embry-type result which classifies the functions f and g such that for any function h commuting with f + g and f * g, we have that h commutes with f and g, too.

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42

GHILONI, RICCARDO, VALTER MORETTI, and ALESSANDRO PEROTTI. "CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES." Reviews in Mathematical Physics 25, no. 04 (May 2013): 1350006. http://dx.doi.org/10.1142/s0129055x13500062.

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The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C*-algebras and to define, on each of these C*-algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.

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43

Colombo, Fabrizio, J. Oscar González-Cervantes, and Irene Sabadini. "The C-property for slice regular functions and applications to the Bergman space." Complex Variables and Elliptic Equations 58, no. 10 (October 2013): 1355–72. http://dx.doi.org/10.1080/17476933.2012.674521.

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44

Colombo, Fabrizio, Daniele Struppa, and Irene Sabadini. "Algebraic properties of the module of slice regular functions in several quaternionic variables." Indiana University Mathematics Journal 61, no. 4 (2012): 1581–602. http://dx.doi.org/10.1512/iumj.2012.61.4978.

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45

Gal, S. G., and I. Sabadini. "Approximation by polynomials in Bergman spaces of slice regular functions in the unit ball." Mathematical Methods in the Applied Sciences 41, no. 4 (December 7, 2017): 1619–30. http://dx.doi.org/10.1002/mma.4689.

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46

Vasilescu, Florian-Horia. "Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions." Concrete Operators 8, no. 1 (January 1, 2021): 90–113. http://dx.doi.org/10.1515/conop-2020-0115.

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Abstract The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.

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47

Alpay, Daniel, Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey. "Functions of the infinitesimal generator of a strongly continuous quaternionic group." Analysis and Applications 15, no. 02 (January 25, 2017): 279–311. http://dx.doi.org/10.1142/s021953051650007x.

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The quaternionic analogue of the Riesz–Dunford functional calculus and the theory of semigroups and groups of linear quaternionic operators have recently been introduced and studied. In this paper, we suppose that [Formula: see text] is the quaternionic infinitesimal generator of a strongly continuous group of operators [Formula: see text] and we show how we can define bounded operators [Formula: see text], where [Formula: see text] belongs to a class of functions that is larger than the one to which the quaternionic functional calculus applies, using the quaternionic Laplace–Stieltjes transform. This class includes functions that are slice regular on the [Formula: see text]-spectrum of [Formula: see text] but not necessarily at infinity. Moreover, we establish the relation between [Formula: see text] and the quaternionic functional calculus and we study the problem of finding the inverse of [Formula: see text].

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48

Ghiloni, Riccardo, and Alessandro Perotti. "Lagrange polynomials over Clifford numbers." Journal of Algebra and Its Applications 14, no. 05 (March 17, 2015): 1550069. http://dx.doi.org/10.1142/s0219498815500693.

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We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions ℍ ≃ ℝ0,2, or to the real Clifford algebra ℝ0,3. In the quaternionic case, the approach by means of Lagrange polynomials is new, and gives a complete solution of the interpolation problem. In the case of ℝ0,3, such a problem is dealt with here for the first time. Elements of the recent theory of slice regular functions are used. Leaving apart the classical cases ℝ0,0 ≃ ℝ, ℝ0,1 ≃ ℂ and the trivial case ℝ1,0 ≃ ℝ⊕ℝ, the interpolation problem on Clifford algebras ℝp,q with (p,q) ≠ (0,2), (0,3) seems to have some intrinsic difficulties.

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49

White, J. A., E. D. Young, and P. B. Manis. "The electrotonic structure of regular-spiking neurons in the ventral cochlear nucleus may determine their response properties." Journal of Neurophysiology 71, no. 5 (May 1, 1994): 1774–86. http://dx.doi.org/10.1152/jn.1994.71.5.1774.

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1. Intracellular recordings were obtained from neurons in parasagittal brain slices of the guinea pig ventral cochlear nucleus (VCN). The principal neurons of the VCN can be parceled into two categories. Regular-spiking (Type I) neurons have a linear current-voltage (I–V) relationship over a large range of intracellularly injected currents and fire tonically in response to suprathreshold depolarizing currents. Phasically spiking (Type II) neurons have a nonlinear I–V relationship and fire only phasically at the onset of a depolarizing current or offset of a hyperpolarizing current. Regular-spiking neurons have been shown to be of the stellate morphological type, whereas phasically spiking neurons have been shown to be bushy cells. 2. The electrotonic structure of regular-spiking neurons was studied by applying previously developed modeling techniques based on the somatic shunt model. In these techniques, physiological data are used to determine the set of parameters best describing the neuron. As predicted from previous theoretical investigations, the use of an anatomic constraint (somatic surface area) reduces the variance in estimates of model parameters, especially for the dendritic membrane time constant tau D. 3. Model representations of regular-spiking cells fall into two categories: those with (passive) somatic membrane properties that are nearly identical to those of the dendrite (8/15 cases), and those with a significant amount of somatic shunt (7/15). Estimates of tau D (mean = 7.7 ms) are lower than those often described in the literature. We argue that this low value of tau D may be related to the need of neurons in the auditory brainstem to operate at high firing rates and/or to encode audio-frequency temporal fluctuations. 4. Dendritic transfer functions were calculated as functions of synaptic location using somatic shunt representations of regular-spiking neurons. These transfer functions allow us to predict that mid-range auditory frequencies (approximately 1 kHz) are greatly attenuated, even for synapses near the soma. Thus it is suggested that the electrotonic architecture of regular-spiking cells creates sufficient low-pass filtering of synaptic inputs to reduce the synchronization of firing of these neurons to mid-frequency auditory stimuli.

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50

Mikulka, Jan. "GPU-Accelerated Reconstruction of T2 Maps in Magnetic Resonance Imaging." Measurement Science Review 15, no. 4 (August 1, 2015): 210–18. http://dx.doi.org/10.1515/msr-2015-0029.

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Abstract The main tissue parameters targeted by MR tomography include, among others, relaxation times T1 and T2. This paper focuses on the computation of the relaxation time T2 measured with the Spin Echo method, where the sensing coil of the tomograph provides a multi-echo signal. The maxima of these echoes must be interleaved with an exponential function, and the T2 relaxation can be determined directly from the exponential waveform. As this procedure needs to be repeated for each pixel of the scanned tissue, the processing of large images then becomes very intensive. For example, given the common resolution of 256×256 with 20 slices and five echoes at different times TE, it is necessary to reconstruct 1.3∙106 exponential functions. At present, such computation performed on a regular PC may last even several minutes. This paper introduces the results provided by accelerated computation based on parallelization and carried out with a graphics card. By using the simple method of linear regression, we obtain a processing time of less than 36 ms. Another effective option consists in the Levenberg-Marquardt algorithm, which enables us to reconstruct the same image in 96 ms. This period is at least 900 times shorter than that achievable with professional software. In this context, the paper also comprises an analysis of the results provided by the above-discussed techniques.

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