Research

     My research interests lie in the area of Wavelets and Frames and their applications, Measure Group Theory, Functional Analysis, and Operator Algebras. 

     My publications can be found on Mathscinet  (institutional subscription required).

1)   Selected Publications:        

• Christoffersen, N.,  Dutkay, D.,  Picioroaga G.,  Weber E.  Parseval frames from compressions of Cuntz algebras. Math. Z. 304, 23 (2023) 

• Dutkay, D.,  Picioroaga, G., Silvestrov, S.  On generalized Walsh bases. Acta Appl. Math. 163 (2019), 73-90.

• Harding, S.N.,  Picioroaga, G.  A generalized Walsh system for arbitrary matrices. Demonstr. Math. 52 (2019), no. 1, 40-55.

•  Picioroaga, G., Weber, E. (2016). Fourier frames for the Cantor-4 set. J. Fourier Anal. Appl. 23 (2017), no. 2, 324-343.

•  Dutkay, D., Picioroaga, G. (2014).  Generalized Walsh Bases and Applications. Acta Appl. Math , 133 (2014), Issue 1, 1-18.

•  Dutkay, D., Han, D., Jorgensen, P., Picioroaga, G. (2013). On common fundamental domains.  Advances in Mathematics, 239, 109-127.

• Dutkay, D., Picioroaga, G., Song, M.-S. Orthonormal bases generated by Cuntz algebras (2014).  Journal of Mathematical Analysis and Applications 409 (2014) 1128-1139.

• Georgescu, C., Picioroaga, G.(2014).  Fuglede-Kadison Determinants For Operators in the von Neumann Algebra of an Equivalence Relation.  Proceedings of the American Mathematical Society 142(2014) 173-180.

• Haagerup, U., Picioroaga, G. (2011). New Presentations of Thompson's Groups and Applications. Journal of Operator Theory/ The Theta Foundation, 66(1), 217-232.

2)   M.S. theses advising :

• •  Steven Nathan Harding (2014-2015),  Generalized Walsh transforms, Cuntz algebras representations and applications in signal processing.

  •  Jasmine Martin (2018-2019), The uncertainty principle and applications to data recovery

  •  Daniel McCarter (2022-2023),  Mathematical analysis of neural networks and examples

3)    Undergraduate Research Projects : 

•  John Aguirre (2013-2014),  Image and sound encryption with Maple .             

• Steven Nathan Harding (2013), Encoding and encryption using generalized Walsh bases.     

• Olivia Roberts (2022-2023),  Understanding musical systems with Z_n Cayley graphs