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Journal articles on the topic 'Slice Regular Functions'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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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 (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 (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 (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 (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 (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 (2016): 861–85. http://dx.doi.org/10.1090/tran/6717.

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8

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 (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.

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9

de Fabritiis, Chiara. "Transcendental operators acting on slice regular functions." Concrete Operators 9, no. 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

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10

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

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11

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

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12

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

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13

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

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14

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

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15

Bisi, Cinzia, and Caterina Stoppato. "Landau’s theorem for slice regular functions on the quaternionic unit ball." International Journal of Mathematics 28, no. 03 (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 generalizatio

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16

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 (2011): 749–59. http://dx.doi.org/10.36045/bbms/1320763135.

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17

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

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18

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

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19

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

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20

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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21

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

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22

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

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23

Altavilla, Amedeo. "On the real differential of a slice regular function." Advances in Geometry 18, no. 1 (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

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24

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 (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 classific

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25

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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26

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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27

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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28

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

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29

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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30

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

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31

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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32

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

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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 (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

Baksa, V., A. Bandura, and O. Skaskiv. "Slice entire functions of quaternionic variable of bounded index." Ukrains’kyi Matematychnyi Zhurnal 77, no. 5 (2025): 295–303. https://doi.org/10.3842/umzh.v77i5.8927.

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UDC 517.55+512.78 We continue our investigations of the local properties of entire slice regular functions of quaternionic variable. For this class of functions, we introduce the notion of index. The boundedness of index is characterized by the local behavior of the maximum modulus of slice derivative on certain discs. The corresponding maximum is uniformly estimated by the value of the modulus of slice derivative at the center of the disc. The presented results are quaternionic generalizations of the known Fricke theorems for entire functions of complex variable.

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35

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 (2015): 1346–65. http://dx.doi.org/10.1080/17476933.2015.1015530.

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36

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

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37

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 (2009): 1793–808. http://dx.doi.org/10.1016/j.aim.2009.06.015.

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38

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

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39

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 (2011): 435–66. http://dx.doi.org/10.1007/s10455-011-9266-0.

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40

Amedeo, Altavilla, and Chiara de Fabritiis. "Applications of the Sylvester operator in the space of slice semi-regular functions." Concrete Operators 7, no. 1 (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 a

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41

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

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42

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 (2015): 1431–55. http://dx.doi.org/10.1080/17476933.2015.1024670.

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43

GHILONI, RICCARDO, VALTER MORETTI, and ALESSANDRO PEROTTI. "CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES." Reviews in Mathematical Physics 25, no. 04 (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.

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44

Linzi, Alessandro. "Polygroup objects in regular categories." AIMS Mathematics 9, no. 5 (2024): 11247–77. http://dx.doi.org/10.3934/math.2024552.

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<abstract><p>We express the fundamental properties of commutative polygroups (also known as canonical hypergroups) in category-theoretic terms, over the category $ \mathbf{Set} $ formed by sets and functions. For this, we employ regularity as well as the monoidal structure induced on the category $ {\mathbf{Rel}} $ of sets and relations by cartesian products. We highlight how our approach can be generalised to any regular category. In addition, we consider the theory of partial multirings and find fully faithful functors between certain slice or coslice categories of the category o

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45

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 (2013): 1355–72. http://dx.doi.org/10.1080/17476933.2012.674521.

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46

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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47

Wani, Irfan Ahmad, and Adil Hussain. "A Note on Location of the Zeros of Quaternionic Polynomials." Armenian Journal of Mathematics 15, no. 7 (2023): 1–12. http://dx.doi.org/10.52737/10.52737/18291163-2023.15.7-1-12.

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The purpose of this paper is to investigate the extensions of the classical Eneström-Kakeya theorem and its various generalizations concerning the distribution of zeros of polynomials from the complex to the quaternionic setting. Using a maximum modulus theorem and the zero set structure in the recently published theory of regular functions and polynomials of a quaternionic variable, we construct new bounds of the Eneström-Kakeya type for the zeros of these polynomials. The obtained results for this subclass of polynomials and slice regular functions give generalizations of a number of results

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48

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 (2017): 1619–30. http://dx.doi.org/10.1002/mma.4689.

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49

Vasilescu, Florian-Horia. "Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions." Concrete Operators 8, no. 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 o

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50

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 (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 transfo

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