Gabriel Picioroaga

Gabriel Picioroaga

Associate Professor

MATHEMATICAL SCIENCES

Patterson Hall 212

Phone: (605) 658-5980

Email: Gabriel.Picioroaga@usd.edu

Website: http://sites.usd.edu/gabriel-picioroaga

Bio:

BS, University of Transylvania, 1992-1997. MS, University of Bucharest, 1997-1998. PhD, The University of Iowa, 1999-2005. Previous professional positions: University of Southern Denmark, 2005-2006. Binghamton University, 2006-2009.


Teaching Interests:

Calculus, Analysis.


Research Interests:

Wavelets and Frames, Measure Group Theory, Functional Analysis, Operator Algebras .


Education:

  • Ph D, Analysis, Operator Algebras, University of Iowa, 2005
  • MS, Real and Complex Analysis, University of Bucharest, 1998
  • BS, Mathematics and Computer Science, The University of Transylvania, 1997

Grants:

  • Research Excellence Grant, The Office of Reseach & College of Arts & Science. (2010 - 2011)

Publications:

Citations listed below are presented in a standardized, modified format for display purposes only. They do not necessarily reflect the preferred style and conventions of the faculty member or discipline.

  • Dutkay, Dorin, Picioroaga, Gabriel, and Silvestrov, Sergei. On Generalized Walsh Bases. Acta Applicandae Mathematicae/Springer, 2018. (DOI: 10.1007/s10440-018-0214-x)
  • Picioroaga, Gabriel, and Weber, Eric. Fourier frames for the Cantor-4 set, 324-343. Vol. 23, Iss. 2. Vienna: Journal of Fourier Analysis and Applications, 2017.
  • Dutkay, Dorin, and Picioroaga, Gabriel. Generalized Walsh Bases and Applications, 1-18. Vol. 133(2014), Iss. 1. Acta Applicandae Mathematicae/Springer, 2014. (DOI: 10.1007/s10440-013-9856-x)
  • Dutkay, Dorin, Picioroaga, Gabriel, and Song, Myung-Sin. Orthonormal bases generated by Cuntz algebras, 1128-1139. Vol. 409 (2014). Journal of Mathematical Analysis and Applications, 2014.
  • Georgescu, Catalin, and Picioroaga, Gabriel. Fuglede-Kadison Determinants For Operators in the von Neumann Algebra of an Equivalence Relation., 173-180. Vol. 142. Proceedings of the American Mathematical Society, 2014.
  • Dutkay, Dorin, Han, Deguang, Jorgensen, Palle, and Picioroaga, Gabriel. On common fundamental domains, 109-127. Vol. 239. Advances in Mathematics, 2013.
  • Haagerup, Uffe, and Picioroaga, Gabriel. New Presentations of Thompson's Groups and Applications, 217-232. Vol. 66, Iss. 1. Bucharest: Journal of Operator Theory/ The Theta Foundation, 2011.
  • Dutkay, Dorin, Han, Deguang, and Picioroaga, Gabriel. Parseval Frames for ICC Groups, 30071-3090. Vol. 256 (2009), Iss. 9. Journal of Functional Analysis, 2009.
  • Dutkay, Dorin, Jorgensen, Palle, and Picioroaga, Gabriel. Unitary Representations of Wavelet Groups and Encodings of Iterated Function Systems in Solenoids, 1815-1852. Vol. 29 (2009), Iss. 6. Cambridge: Ergodic Theory and Dynamical Systems, 2009.
  • Dutkay, Dorin, Han, Deguang, Picioroaga, Gabriel, and Sun, Qiyu. Orthonormal Dilations of Parseval Wavelets, 483-515. Vol. 341 (2008), Iss. 3. Mathematische Annalen, 2008.
  • Chifan, Ionut, and Picioroaga, Gabriel. C* Estimates for Averaging Sums of Elements in the Thompson Group F. In Perspectives in Operator Algebras and Mathematical Physics, 41-51. Vol. 8. Bucharest: Theta Series in Advanced Mathematics, 2008.
  • Dutkay, Dorin, and Picioroaga, Gabriel. The Von Neumann Algebra of the Canonical Equivalence Relation of the Thompson Group. In Operator theory 20. Vol. 6 (2006). Bucharest: Theta Series in Advanced Mathematics, 2006.
  • Picioroaga, Gabriel. The Inner Amenability of the Generalized Thompson Group, 1995-2002. Vol. 134 (2006), Iss. 7. Proc. Amer. Math. Soc., 2005.
  • Bildea, Stefan, Dutkay, Dorin, and Picioroaga, Gabriel. MRA Superwavelets, 1-19. Vol. 11 (2005). Albany, NY: New York Journal of Mathematics, 2005.

Presentations:

  • Picioroaga, Gabriel. Frames and orthonormal bases generated by Cuntz systems. Presented at the Special Session on Applied Harmonic Analysis: Frame Theory and Applications, AMS, San Francisco , CA. (October 27, 2018)
  • Picioroaga, Gabriel. Generalized Walsh bases and some applications to digital signal processing. Presented at the Smooth and Non Smooth Harmonic Analysis, Ames, Iowa. (June 3, 2018)
  • Picioroaga, Gabriel. On Generalized Walsh Orthonormal Bases. Presented at the Special Session on Applied Harmonic Analysis:Frames, Samplings and Applications at the American Mathematical Society , Orlando, Florida. (September 24, 2017)
  • Picioroaga, Gabriel. Fourier Frames for the Cantor-4 Set. Presented at the Special Session on Frames, Harmonic Analysis, and Operator Theory for the 1120th American Mathematical Society , North Dakota State University. (April 17, 2016)
  • Picioroaga, Gabriel. Cuntz, Walsh and Wavelet Transforms. Presented at the Analysis Seminar, Ames, IA. (March 25, 2015)
  • Harding, Steven N., Picioroaga, Gabriel. Data encryption using Cuntz algebras representations. Presented at the MAA Nebraska/SE South Dakota Section MAA, Nebraska Wesleyan University, Lincoln, Nebraska. (March 14, 2014)
  • Picioroaga, Gabriel. Cuntz algebras, generalized Walsh bases and applications. Presented at the INFAS (Iowa-Nebraska Functional Analysis Seminar), Des Moines, IA. (November 9, 2013)
  • Picioroaga, Gabriel. Cuntz algebras, generalized Walsh bases and applications. Presented at the Colloquium, Mathematics Department, University of Central Florida, October 31. (October 31, 2013)
  • Picioroaga, Gabriel. Orthonormal bases generated by Cuntz algebras. Presented at the Operator Theory Seminar, University of Iowa, October 15. (October 15, 2013)
  • Picioroaga, Gabriel. Orthonormal bases generated by Cuntz algebras. Presented at the Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings', 1089th AMS Meeting, University of Colorado Boulder, April 13-14. (April 13, 2013)
  • Georgescu, Catalin, Picioroaga, Gabriel. Fuglede-Kadison Determinants For Operators In The Von Neumann Algebra Of An Equivalence Relation.. Presented at the 1074th AMS Sectional Meeting, University of Nebraska Lincoln.. (October 14, 2011)
  • Georgescu, Catalin, Picioroaga, Gabriel. Fuglede-Kadison Determinants For Operators In The Von Neumann Algebra Of An Equivalence Relation.. Presented at the Great Plains Operator Theory Symposium 2011, Arizona State University. (May 18, 2011)
  • Picioroaga, Gabriel. On Common Fundamental Domains. Presented at the AMS Spring Central Sectional Meeting, St.Paul, MN. (April 10, 2010)