Cho, Ilwoo Free probability on Banach algebras induced by scaled hypercomplex numbers. (English) Zbl 07818527 Complex Anal. Oper. Theory 18, No. 2, Paper No. 27, 52 p. (2024). MSC: 46S10 47S10 20G20 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 18, No. 2, Paper No. 27, 52 p. (2024; Zbl 07818527) Full Text: DOI
Alpay, Daniel; Cho, Ilwoo Certain invertible operator-block matrices induced by \(C^*\)-algebras and scaled hypercomplex numbers. (English) Zbl 07771750 Res. Math. Sci. 10, No. 4, Paper No. 47, 44 p. (2023). Reviewer: Huang Wenxue (Scarborough) MSC: 20G20 46G20 46S10 47S10 PDFBibTeX XMLCite \textit{D. Alpay} and \textit{I. Cho}, Res. Math. Sci. 10, No. 4, Paper No. 47, 44 p. (2023; Zbl 07771750) Full Text: DOI OA License
Cho, Ilwoo Free random variables followed by the semicircular law. (English) Zbl 07757930 Complex Anal. Oper. Theory 17, No. 7, Paper No. 116, 45 p. (2023). MSC: 46L54 46L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 17, No. 7, Paper No. 116, 45 p. (2023; Zbl 07757930) Full Text: DOI
Alpay, Daniel; Cho, Ilwoo Operators induced by certain hypercomplex systems. (English) Zbl 1526.46051 Opusc. Math. 43, No. 3, 275-333 (2023). MSC: 46S10 47S10 PDFBibTeX XMLCite \textit{D. Alpay} and \textit{I. Cho}, Opusc. Math. 43, No. 3, 275--333 (2023; Zbl 1526.46051) Full Text: DOI arXiv
Alpay, Daniel; Cho, Ilwoo Dynamical systems of operators induced by scaled hypercomplex rings. (English) Zbl 1525.46046 Adv. Appl. Clifford Algebr. 33, No. 3, Paper No. 33, 39 p. (2023). MSC: 46L55 46S10 47S10 PDFBibTeX XMLCite \textit{D. Alpay} and \textit{I. Cho}, Adv. Appl. Clifford Algebr. 33, No. 3, Paper No. 33, 39 p. (2023; Zbl 1525.46046) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle Comparing Banach spaces for systems of free random variables followed by the semicircular law. (English) Zbl 07678118 Aron, Richard M. (ed.) et al., Operator and norm inequalities and related topics. Cham: Birkhäuser. Trends Math., 773-822 (2022). MSC: 47A30 47A50 47A63 46B20 47B35 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. Jorgensen}, in: Operator and norm inequalities and related topics. Cham: Birkhäuser. 773--822 (2022; Zbl 07678118) Full Text: DOI
Cho, Ilwoo Group dynamical systems on \(C^*\)-algebras generated by countable infinitely many semicircular elements. (English) Zbl 1483.46066 Singh, Jagdev (ed.) et al., Methods of mathematical modelling and computation for complex systems. Cham: Springer. Stud. Syst. Decis. Control 373, 159-205 (2022). MSC: 46L54 46L55 PDFBibTeX XMLCite \textit{I. Cho}, Stud. Syst. Decis. Control 373, 159--205 (2022; Zbl 1483.46066) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Multi variable semicircular processes from \(\ast\)-homomorphisms and operators. (English) Zbl 1510.46040 Alpay, Daniel (ed.) et al., New directions in function theory: from complex to hypercomplex to non-commutative. Selected papers based on the presentations at the conference, Chapman University, Orange, CA, USA, November 21–26, 2019. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 286, 199-242 (2021). MSC: 46L54 46L10 46L40 46L53 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Oper. Theory: Adv. Appl. 286, 199--242 (2021; Zbl 1510.46040) Full Text: DOI
Cho, Ilwoo Spectral properties of certain operators on the free Hilbert space \(\mathfrak{F}[H_1,\ldots,H_N]\) and the semicircular law. (English) Zbl 1493.46077 Opusc. Math. 41, No. 6, 755-803 (2021). MSC: 46L10 46L54 47L30 47L55 47B02 PDFBibTeX XMLCite \textit{I. Cho}, Opusc. Math. 41, No. 6, 755--803 (2021; Zbl 1493.46077) Full Text: DOI
Cho, Ilwoo Free Poisson elements induced by orthogonal projections. (English) Zbl 1482.05342 Paikray, Susanta Kumar (ed.) et al., New trends in applied analysis and computational mathematics. Proceedings of the international conference on advances in mathematics and computing, ICAMC 2020, Odisha, India, February 7–8, 2020. Singapore: Springer. Adv. Intell. Syst. Comput. 1356, 191-234 (2021). MSC: 05E14 11R56 46L54 47L30 47L55 17B63 PDFBibTeX XMLCite \textit{I. Cho}, Adv. Intell. Syst. Comput. 1356, 191--234 (2021; Zbl 1482.05342) Full Text: DOI
Cho, Ilwoo Free-homomorphic relations on Banach \(*\)-probability spaces generated by semicircular elements induced by natural numbers. (English) Zbl 1478.46058 Complex Anal. Oper. Theory 15, No. 3, Paper No. 53, 44 p. (2021). MSC: 46L53 46L54 46L10 46L40 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 15, No. 3, Paper No. 53, 44 p. (2021; Zbl 1478.46058) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle Free-homomorphic relations induced by certain free semicircular families. (English) Zbl 1469.46059 Alpay, Daniel (ed.) et al., Complex function theory, operator theory, Schur analysis and systems theory. A volume in honor of V. E. Katsnelson. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 280, 229-285 (2020). MSC: 46L54 46L40 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. Jorgensen}, Oper. Theory: Adv. Appl. 280, 229--285 (2020; Zbl 1469.46059) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Certain \(*\)-homomorphisms of \(C^*\)-algebras and sequences of semicircular elements: a Banach space view. (English) Zbl 1465.46065 Ill. J. Math. 64, No. 4, 519-567 (2020). MSC: 46L54 46L10 47L55 47L65 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Ill. J. Math. 64, No. 4, 519--567 (2020; Zbl 1465.46065) Full Text: DOI Euclid
Cho, Ilwoo Certain \(\ast\)-homomorphisms acting on unital \(C^\ast\)-probability spaces and semicircular elements induced by \(p\)-adic number fields over primes \(p\). (English) Zbl 1456.46053 Electron. Res. Arch. 28, No. 2, 739-776 (2020). MSC: 46L54 47L30 11R56 47L55 47S10 PDFBibTeX XMLCite \textit{I. Cho}, Electron. Res. Arch. 28, No. 2, 739--776 (2020; Zbl 1456.46053) Full Text: DOI
Cho, Ilwoo Circular-like and circular elements in free product Banach \({*}\)-algebras induced by \(p\)-adic number fields \(\mathbb{Q}_p\) over primes \(p\). (English) Zbl 1439.46052 Dutta, Hemen (ed.) et al., Applied mathematical analysis: theory, methods, and applications. Cham: Springer. Stud. Syst. Decis. Control 177, 605-654 (2020). MSC: 46L54 46L53 11R56 46L09 PDFBibTeX XMLCite \textit{I. Cho}, Stud. Syst. Decis. Control 177, 605--654 (2020; Zbl 1439.46052) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Deformation of semicircular and circular laws via \(p\)-adic number fields and sampling of primes. (English) Zbl 1452.46052 Opusc. Math. 39, No. 6, 773-813 (2019). MSC: 46L54 46S10 47L30 47L55 60B05 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Opusc. Math. 39, No. 6, 773--813 (2019; Zbl 1452.46052) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle Free probability on \( C^*\)-algebras induced by Hecke algebras over primes. (English) Zbl 1450.46049 Discrete Contin. Dyn. Syst., Ser. S 12, No. 8, 2221-2252 (2019). MSC: 46L54 46L53 46S10 47L55 05E16 11R56 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. Jorgensen}, Discrete Contin. Dyn. Syst., Ser. S 12, No. 8, 2221--2252 (2019; Zbl 1450.46049) Full Text: DOI
Cho, Ilwoo Certain Banach-space operators acting on the semicircular elements induced by orthogonal projections. (English) Zbl 1435.47047 Singh, Jagdev (ed.) et al., Mathematical modelling, applied analysis and computation. Selected papers of the first international conference, ICMMAAC 2018, JECRC University, Jaipur, India, July 6–8, 2018. Singapore: Springer. Springer Proc. Math. Stat. 272, 1-39 (2019). Reviewer: Elhadj Dahia (Elhamel) MSC: 47C05 47B01 47B37 46L54 46B28 PDFBibTeX XMLCite \textit{I. Cho}, Springer Proc. Math. Stat. 272, 1--39 (2019; Zbl 1435.47047) Full Text: DOI
Cho, Ilwoo Banach-space operators acting on semicircular elements induced by orthogonal projections. (English) Zbl 1459.46053 Complex Anal. Oper. Theory 13, No. 8, 4065-4115 (2019). MSC: 46L10 46L40 46L53 46L54 47L15 47L30 47L55 47B01 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 13, No. 8, 4065--4115 (2019; Zbl 1459.46053) Full Text: DOI
Cho, Ilwoo Asymptotic semicircular law induced by \(p\)-adic number fields \(\mathbb{Q}_p\) over primes. (English) Zbl 1428.11102 Complex Anal. Oper. Theory 13, No. 7, 3169-3206 (2019). MSC: 11F85 11G15 11R47 11R56 46L10 46L54 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 13, No. 7, 3169--3206 (2019; Zbl 1428.11102) Full Text: DOI
Cho, Ilwoo Semicircular-like and semicircular laws on Banach \(*\)-probability spaces induced by dynamical systems of the finite adele ring \(A_{\mathbb{Q}}\). (English) Zbl 06946443 Adv. Oper. Theory 4, No. 1, 24-70 (2019). MSC: 47L30 47L55 11R47 11R56 46L54 PDFBibTeX XMLCite \textit{I. Cho}, Adv. Oper. Theory 4, No. 1, 24--70 (2019; Zbl 06946443) Full Text: DOI Euclid
Cho, Ilwoo Adelic analysis and functional analysis on the finite adele ring. (English) Zbl 1409.46038 Opusc. Math. 38, No. 2, 139-185 (2018). MSC: 46L54 05E15 11G15 11R47 11R56 46L10 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Opusc. Math. 38, No. 2, 139--185 (2018; Zbl 1409.46038) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Analysis of free products of the general linear groups \(\mathrm{GL}_{2}(\mathbb{Q}_{p})\) and Hecke algebras \(\mathcal{H}( \mathrm{GL}_{2}(\mathbb{Q}_{p})) \) over primes \(p\). (English) Zbl 1443.20040 Christensen, Jens Gerlach (ed.) et al., Representation theory and harmonic analysis on symmetric spaces. AMS special session on harmonic analysis, in honor of Gestur Ólafsson’s 65th birthday, Atlanta, GA, USA, January 4, 2017. Proceedings. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 714, 23-75 (2018). MSC: 20E06 20C08 46L54 46L40 46L53 47L55 05E16 20G15 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Contemp. Math. 714, 23--75 (2018; Zbl 1443.20040) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Banach \(^*\)-algebras generated by semicircular elements induced by certain orthogonal projections. (English) Zbl 1406.46054 Opusc. Math. 38, No. 4, 501-535 (2018). MSC: 46L54 47L15 47L30 47L55 46K05 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Opusc. Math. 38, No. 4, 501--535 (2018; Zbl 1406.46054) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. A harmonic analysis of directed graphs from arithmetic functions and primes. (English) Zbl 1432.11105 Pesenson, Isaac (ed.) et al., Recent applications of harmonic analysis to function spaces, differential equations, and data science. Novel methods in harmonic analysis. Volume 2. Cham: Birkhäuser/Springer. Appl. Numer. Harmon. Anal., 603-651 (2017). MSC: 11K65 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, in: Recent applications of harmonic analysis to function spaces, differential equations, and data science. Novel methods in harmonic analysis. Volume 2. Cham: Birkhäuser/Springer. 603--651 (2017; Zbl 1432.11105) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Free products of \(C^*\)-probability spaces from \(p\)-adic Hecke algebras. (English) Zbl 1392.46049 Colombo, Fabrizio (ed.) et al., Advances in complex analysis and operator theory. Festschrift in honor of Daniel Alpay’s 60th birthday. Contributions partly based on the presentations at the international conference on complex analysis and operator theory, Chapman University, Orange, CA, USA, November 2016. Cham: Birkhäuser/Springer (ISBN 978-3-319-62361-0/hbk; 978-3-319-62362-7/ebook). Trends in Mathematics, 55-99 (2017). MSC: 46L54 05E15 11R56 46L10 46L09 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, in: Advances in complex analysis and operator theory. Festschrift in honor of Daniel Alpay's 60th birthday. Contributions partly based on the presentations at the international conference on complex analysis and operator theory, Chapman University, Orange, CA, USA, November 2016. Cham: Birkhäuser/Springer. 55--99 (2017; Zbl 1392.46049) Full Text: DOI
Cho, Ilwoo Free probability on \(W^{*}\)-dynamical systems determined by \(GL_{2}(\mathbb {Q} _{p})\): generalized Hecke algebras. (English) Zbl 1392.46048 Boll. Unione Mat. Ital. 10, No. 4, 725-764 (2017). MSC: 46L54 05E15 46L10 46L40 11R56 11R99 46L55 PDFBibTeX XMLCite \textit{I. Cho}, Boll. Unione Mat. Ital. 10, No. 4, 725--764 (2017; Zbl 1392.46048) Full Text: DOI
Cho, Ilwoo Free semicircular families in free product Banach \(\ast\)-algebras induced by \(p\)-adic number fields over primes \(p\). (English) Zbl 1359.05138 Complex Anal. Oper. Theory 11, No. 3, 507-565 (2017). MSC: 05E15 11G15 11R47 11R56 46L10 46L54 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 11, No. 3, 507--565 (2017; Zbl 1359.05138) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Krein-space operators determined by free product algebras induced by primes and graphs. (English) Zbl 1358.05309 Spec. Matrices 5, 1-35 (2017). MSC: 05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Spec. Matrices 5, 1--35 (2017; Zbl 1358.05309) Full Text: DOI
Cho, Ilwoo; Gillespie, Timothy; Jorgensen, Palle E. T. Asymptotic free probability for arithmetic functions and factorization of Dirichlet series. (English) Zbl 1353.05126 Anal. Math. Phys. 6, No. 3, 255-295 (2016). MSC: 05E15 11G15 11R04 11R09 11R47 11R56 46L54 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho} et al., Anal. Math. Phys. 6, No. 3, 255--295 (2016; Zbl 1353.05126) Full Text: DOI
Cho, Ilwoo Factorization of \(\mathbb C\)-valued functions induced by graphs. (English) Zbl 1353.05125 Complex Anal. Oper. Theory 10, No. 7, 1453-1499 (2016). MSC: 05E15 05C20 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 10, No. 7, 1453--1499 (2016; Zbl 1353.05125) Full Text: DOI
Cho, Ilwoo Free probability on Hecke algebras and certain group \(C^{*}\)-algebras induced by Hecke algebras. (English) Zbl 1339.05426 Opusc. Math. 36, No. 2, 153-187 (2016). MSC: 05E15 05E10 11R47 46L54 47L15 47L55 20C08 46L05 PDFBibTeX XMLCite \textit{I. Cho}, Opusc. Math. 36, No. 2, 153--187 (2016; Zbl 1339.05426) Full Text: DOI
Cho, Ilwoo Certain group dynamical systems induced by Hecke algebras. (English) Zbl 1335.05213 Opusc. Math. 36, No. 3, 337-373 (2016). MSC: 05E15 11R47 46L10 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Opusc. Math. 36, No. 3, 337--373 (2016; Zbl 1335.05213) Full Text: DOI
Cho, Ilwoo Representations and corresponding operators induced by Hecke algebras. (English) Zbl 1332.05152 Complex Anal. Oper. Theory 10, No. 3, 437-477 (2016). MSC: 05E15 05E10 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 10, No. 3, 437--477 (2016; Zbl 1332.05152) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Free \(W^*\)-dynamical systems from \(p\)-adic number fields and the Euler totient function. (English) Zbl 1346.46058 Mathematics 3, No. 4, 1095-1138 (2015). MSC: 46L54 46S10 11A25 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Mathematics 3, No. 4, 1095--1138 (2015; Zbl 1346.46058) Full Text: DOI
Cho, Ilwoo On dynamical systems induced by \(p\)-adic number fields. (English) Zbl 1326.05170 Opusc. Math. 35, No. 4, 445-484 (2015). MSC: 46L55 11R56 37A55 37P20 46L54 47L15 PDFBibTeX XMLCite \textit{I. Cho}, Opusc. Math. 35, No. 4, 445--484 (2015; Zbl 1326.05170) Full Text: DOI
Cho, Ilwoo; Gillespie, Timothy L. Free probability on Hecke algebras. (English) Zbl 1325.11127 Complex Anal. Oper. Theory 9, No. 7, 1491-1531 (2015). MSC: 46L54 05E15 46L10 46L40 46L53 47L55 47S10 PDFBibTeX XMLCite \textit{I. Cho} and \textit{T. L. Gillespie}, Complex Anal. Oper. Theory 9, No. 7, 1491--1531 (2015; Zbl 1325.11127) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs. (English) Zbl 1319.05150 Spec. Matrices 3, 123-154 (2015). MSC: 05E18 05E15 05C20 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Spec. Matrices 3, 123--154 (2015; Zbl 1319.05150) Full Text: DOI
Cho, Ilwoo \(\mathbb C\)-valued functions induced by graphs. (English) Zbl 1314.05228 Complex Anal. Oper. Theory 9, No. 3, 519-565 (2015). MSC: 05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 9, No. 3, 519--565 (2015; Zbl 1314.05228) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Krein-space representations of arithmetic functions determined by primes. (English) Zbl 1305.05233 Algebr. Represent. Theory 17, No. 6, 1809-1841 (2014). MSC: 05E15 05E10 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Algebr. Represent. Theory 17, No. 6, 1809--1841 (2014; Zbl 1305.05233) Full Text: DOI