Colombo, Fabrizio; Kimsey, David P. A survey on the recent advances in the spectral theory on the S-spectrum. (English) Zbl 07691550 Alpay, Daniel (ed.) et al., Recent developments in operator theory, mathematical physics and complex analysis. Proceedings of the 32nd international workshop on operator theory and its applications, IWOTA 2021, Chapman University, Orange, CA, USA, August 9–13, 2022. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 290, 115-170 (2023). MSC: 47S05 47A10 PDFBibTeX XMLCite \textit{F. Colombo} and \textit{D. P. Kimsey}, Oper. Theory: Adv. Appl. 290, 115--170 (2023; Zbl 07691550) Full Text: DOI
Wang, Chao; Qin, Guangzhou; Agarwal, Ravi P. Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem. (English) Zbl 07622192 Adv. Math. 410, Part B, Article ID 108747, 97 p. (2022). MSC: 47A10 47A60 47A55 47D06 PDFBibTeX XMLCite \textit{C. Wang} et al., Adv. Math. 410, Part B, Article ID 108747, 97 p. (2022; Zbl 07622192) Full Text: DOI
Colombo, Fabrizio; De Martino, Antonino; Qian, Tao; Sabadini, Irene The Poisson kernel and the Fourier transform of the slice monogenic Cauchy kernels. (English) Zbl 1486.30133 J. Math. Anal. Appl. 512, No. 1, Article ID 126115, 23 p. (2022). MSC: 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., J. Math. Anal. Appl. 512, No. 1, Article ID 126115, 23 p. (2022; Zbl 1486.30133) Full Text: DOI arXiv
Colombo, Fabrizio; Kimsey, David P. The spectral theorem for normal operators on a Clifford module. (English) Zbl 07452163 Anal. Math. Phys. 12, No. 1, Paper No. 25, 92 p. (2022). MSC: 47A10 47A60 PDFBibTeX XMLCite \textit{F. Colombo} and \textit{D. P. Kimsey}, Anal. Math. Phys. 12, No. 1, Paper No. 25, 92 p. (2022; Zbl 07452163) Full Text: DOI arXiv
Dou, Xinyuan; Jin, Ming; Ren, Guangbin; Sabadini, Irene A new approach to slice analysis via slice topology. (English) Zbl 1482.30118 Adv. Appl. Clifford Algebr. 31, No. 5, Paper No. 67, 36 p. (2021). Reviewer: María Elena Luna Elizarrarás (Holon) MSC: 30G35 32D05 PDFBibTeX XMLCite \textit{X. Dou} et al., Adv. Appl. Clifford Algebr. 31, No. 5, Paper No. 67, 36 p. (2021; Zbl 1482.30118) Full Text: DOI arXiv
Colombo, Fabrizio; Gantner, Jonathan; Pinton, Stefano An introduction to hyperholomorphic spectral theories and fractional powers of vector operators. (English) Zbl 07384103 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 45, 37 p. (2021). Reviewer: Florian-Horia Vasilescu (Villeneuve d’Ascq) MSC: 47A10 47A60 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 45, 37 p. (2021; Zbl 07384103) Full Text: DOI arXiv
Alpay, Daniel; Bolotnikov, Vladimir; Colombo, Fabrizio; Sabadini, Irene Interpolation problems for certain classes of slice hyperholomorphic functions. (English) Zbl 1353.30049 Integral Equations Oper. Theory 86, No. 2, 165-183 (2016). MSC: 30G35 30E05 PDFBibTeX XMLCite \textit{D. Alpay} et al., Integral Equations Oper. Theory 86, No. 2, 165--183 (2016; Zbl 1353.30049) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene Slice hyperholomorphic functional calculi. (English) Zbl 1334.47018 Alpay, Daniel (ed.), Operator theory. With 51 figures and 2 tables. In 2 volumes. Basel: Springer (ISBN 978-3-0348-0666-4/print; 978-3-0348-0667-1/ebook; 978-3-0348-0668-8/print+ebook; 978-3-0348-0692-3/online (updated continuously)). Springer Reference, 1787-1821 (2015). Reviewer: Piotr Niemiec (Kraków) MSC: 47A60 46S10 47-02 30G35 PDFBibTeX XMLCite \textit{F. Colombo} and \textit{I. Sabadini}, in: Operator theory. With 51 figures and 2 tables. In 2 volumes. Basel: Springer. 1787--1821 (2015; Zbl 1334.47018) Full Text: DOI Link
Ren, Guangbin; Xu, Zhenghua Schwarz’s lemma for slice Clifford analysis. (English) Zbl 1327.15053 Adv. Appl. Clifford Algebr. 25, No. 4, 965-976 (2015). MSC: 15A66 PDFBibTeX XMLCite \textit{G. Ren} and \textit{Z. Xu}, Adv. Appl. Clifford Algebr. 25, No. 4, 965--976 (2015; Zbl 1327.15053) Full Text: DOI
Gal, Sorin G.; Sabadini, Irene Universality properties of the quaternionic power series and entire functions. (English) Zbl 1318.30081 Math. Nachr. 288, No. 8-9, 917-924 (2015). MSC: 30G35 30B30 30E10 PDFBibTeX XMLCite \textit{S. G. Gal} and \textit{I. Sabadini}, Math. Nachr. 288, No. 8--9, 917--924 (2015; Zbl 1318.30081) Full Text: DOI
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene Krein-Langer factorization and related topics in the slice hyperholomorphic setting. (English) Zbl 1314.47036 J. Geom. Anal. 24, No. 2, 843-872 (2014). Reviewer: Vladimir V. Peller (East Lansing) MSC: 47B32 47S10 30G35 PDFBibTeX XMLCite \textit{D. Alpay} et al., J. Geom. Anal. 24, No. 2, 843--872 (2014; Zbl 1314.47036) Full Text: DOI arXiv
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus The inverse Fueter mapping theorem in integral form using spherical monogenics. (English) Zbl 1341.30042 Isr. J. Math. 194, Part A, 485-505 (2013). Reviewer: Regina de Almeida (Vila Real) MSC: 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Isr. J. Math. 194, Part A, 485--505 (2013; Zbl 1341.30042) Full Text: DOI Link
Vajiac, Mihaela B. The \( S \)-spectrum for some classes of matrices. (English) Zbl 1262.30060 Gentili, Graziano (ed.) et al., Advances in hypercomplex analysis. Based on the INdAM workshop on different notions of regularity for functions of a quaternionic variable, Rome, Italy, September 13–17, 2010. Berlin: Springer (ISBN 978-88-470-2444-1/hbk; 978-88-470-2445-8/ebook). Springer INdAM Series 1, 125-139 (2013). MSC: 30G35 PDFBibTeX XMLCite \textit{M. B. Vajiac}, Springer INdAM Ser. 1, 125--139 (2013; Zbl 1262.30060) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene Some remarks on the \(\mathcal S\)-spectrum. (English) Zbl 1277.47007 Complex Var. Elliptic Equ. 58, No. 1, 1-6 (2013). Reviewer: Mohammad Bagher Ghaemi (Tehran) MSC: 47A10 47A60 30G35 PDFBibTeX XMLCite \textit{F. Colombo} and \textit{I. Sabadini}, Complex Var. Elliptic Equ. 58, No. 1, 1--6 (2013; Zbl 1277.47007) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniele C. Sheaves of slice regular functions. (English) Zbl 1254.30081 Math. Nachr. 285, No. 8-9, 949-958 (2012). MSC: 30G35 18F20 PDFBibTeX XMLCite \textit{F. Colombo} et al., Math. Nachr. 285, No. 8--9, 949--958 (2012; Zbl 1254.30081) Full Text: DOI arXiv
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene Schur functions and their realizations in the slice hyperholomorphic setting. (English) Zbl 1258.47018 Integral Equations Oper. Theory 72, No. 2, 253-289 (2012). Reviewer: Florian-Horia Vasilescu (Villeneuve d’Ascq) MSC: 47A48 30G35 46E22 93B28 PDFBibTeX XMLCite \textit{D. Alpay} et al., Integral Equations Oper. Theory 72, No. 2, 253--289 (2012; Zbl 1258.47018) Full Text: DOI arXiv
Colombo, Fabrizio; Gonzàles Cervantes, Jose O.; Sabadini, Irene The Bergman-Sce transform for slice monogenic functions. (English) Zbl 1253.30078 Math. Methods Appl. Sci. 34, No. 15, 1896-1909 (2011). MSC: 30H05 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Math. Methods Appl. Sci. 34, No. 15, 1896--1909 (2011; Zbl 1253.30078) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene The quaternionic evolution operator. (English) Zbl 1220.47056 Adv. Math. 227, No. 5, 1772-1805 (2011). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 47D06 47A60 47A10 PDFBibTeX XMLCite \textit{F. Colombo} and \textit{I. Sabadini}, Adv. Math. 227, No. 5, 1772--1805 (2011; Zbl 1220.47056) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniele C. The Runge theorem for slice hyperholomorphic functions. (English) Zbl 1220.30068 Proc. Am. Math. Soc. 139, No. 5, 1787-1803 (2011). Reviewer: Vasily A. Chernecky (Odessa) MSC: 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Proc. Am. Math. Soc. 139, No. 5, 1787--1803 (2011; Zbl 1220.30068) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniele C. The Pompeiu formula for slice hyperholomorphic functions. (English) Zbl 1246.30079 Mich. Math. J. 60, No. 1, 163-170 (2011). Reviewer: Vladislav V. Kravchenko (Queretaro) MSC: 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Mich. Math. J. 60, No. 1, 163--170 (2011; Zbl 1246.30079) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene; Sommen, Frank The Fueter mapping theorem in integral form and the \(\mathcal F\)-functional calculus. (English) Zbl 1225.47019 Math. Methods Appl. Sci. 33, No. 17, 2050-2066 (2010). Reviewer: Alan J. Pryde (Clayton) MSC: 47A60 47A10 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Math. Methods Appl. Sci. 33, No. 17, 2050--2066 (2010; Zbl 1225.47019) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniele C. An extension theorem for slice monogenic functions and some of its consequences. (English) Zbl 1213.30085 Isr. J. Math. 177, 369-389 (2010). Reviewer: Wolfgang Sprößig (Freiberg) MSC: 30G35 PDFBibTeX XMLCite \textit{F. Colombo} et al., Isr. J. Math. 177, 369--389 (2010; Zbl 1213.30085) Full Text: DOI
Colombo, Fabrizio; Sabadini, Irene On the formulations of the quaternionic functional calculus. (English) Zbl 1220.47022 J. Geom. Phys. 60, No. 10, 1490-1508 (2010). Reviewer: Bebe Prunaru (Bucureşti) MSC: 47A60 47A10 30G35 PDFBibTeX XMLCite \textit{F. Colombo} and \textit{I. Sabadini}, J. Geom. Phys. 60, No. 10, 1490--1508 (2010; Zbl 1220.47022) Full Text: DOI