RESEARCH
I wrote my thesis under the supervision of Prof. Christopher Heil. (Here is a link to a PDF file of my thesis ). My research interests include:
Harmonic analysis, especially time-frequency analysis and wavelet analysis, frames theory.
Linear and bilinear pseudodifferential operators
Analysis on fractals
Here is my research statement for more details about my current and future research plans: statement .
Generalized eigenfunctions and a Borel theorem on the Sierpinski gasket (with L. G. Rogers and R. S. Strichartz), [pdf], submitted for publication.
Time-frequency estimates for pseudodifferential operators (with A. Benyi), [pdf] , submitted for publicdation.
Asymptotics of eigenvalue clusters for Schrodinger operators on the Sierpinski gasket (with R. S. Strichartz), [pdf], [ps] , submitted for publication.
An uncertainty principle for graphs, fractals and manifold (with A. Teplyaev), [pdf], [ps], submitted for publication.
Multilinear localization operators (with E. Cordero), [pdf], [ps], to appear in Journal of Mathematical Analysis and Applications.
Modulation spaces estimates for multilinear pseudodifferential operators (with A. Benyi), [pdf]; [ps], Studia Math., 172 (2006), no. 2, 169-180.
Modulation spaces and a class of bounded multilinear pseudodifferential operators (with A. Benyi, K. Grochenig and C. Heil), [pdf]; [ps], J. Operator Theory, 54 (2005), no. 2, 389-401.
A class of Fourier multipliers for modulation spaces, (with A. Benyi, L. Grafakos and K. Grochenig), [ps],; [pdf], Appl. Comput. Harmon. Anal. 19 (2005), no 1, 131-139.
Convolutional frames and the frame potential, (with M. Fickus, B.D. Johnson and K. Kornelson), [pdf]; [ps], Appl. Comput. Harmon. Anal. 19 (2005), no 1, 77-91.
Weak uncertainty principles on fractals (with R. S. Strichartz), [pdf]; [ps], J. Fourier Anal. Appl. 11 (2005), no 3, 315-331.
Bilinear pseudodifferential operators on modulation spaces (with A. Benyi), [pdf], J. Fourier Anal. Appl. 10 (2004), no 3, 301-313. .
Embeddings of some classical Banach spaces into the modulation spaces, [pdf], Proc. Amer. Math. Soc. 132 (2004), no. 6, 1639-1647.
Gabor analysis in weighted amalgam spaces (with K. Grochenig and C. Heil), [pdf], Sampl. Theory Image Signal Process. 1 (2003), no. 3, 225-260.