By Radu Balan, Matthew Begué, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou

This quantity includes contributions spanning a large spectrum of harmonic research and its functions written by way of audio system on the February Fourier Talks from 2002 – 2013. Containing state-of-the-art effects via a magnificent array of mathematicians, engineers and scientists in academia, and executive, it is going to be a superb reference for graduate scholars, researchers and execs in natural and utilized arithmetic, physics and engineering. issues lined include:

specified themes in Harmonic Analysis

Applications and Algorithms within the actual Sciences

Gabor Theory

RADAR and Communications: layout, conception, and Applications

The February Fourier Talks are held every year on the Norbert Wiener middle for Harmonic research and purposes. situated on the collage of Maryland, university Park, the Norbert Wiener middle offers a state-of- the-art learn venue for the large rising region of mathematical engineering.

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H. Koch, D. Tataru, A priori bounds for the 1D cubic NLS in negative Sobolev spaces. Int. Math. Res. Not. IMRN 2007(16), Art. ID rnm053, 36 pp (2007) 36. J. L¨uhrmann, D. Mendelson, Random data Cauchy theory for nonlinear wave equations of power-type on R3 . Commun. Partial Differ. Equs. 39(12), 2262–2283 (2014) 37. A. Nahmod, G. Staffilani, Almost sure well-posedness for the periodic 3D quintic NLS below the energy space. J. Eur. Math. Soc. (2012, to appear) 38. A. Nahmod, N. Pavlovi´c, G. Staffilani, Almost sure existence of global weak solutions for supercritical Navier-Stokes equations.

Oh, O. Pocovnicu, On the probabilistic Cauchy theory of the cubic nonlinear 3. A. Schr¨odinger equation on Rd , d ≥ 3. Trans. Am. Math. Soc. Ser. B 2, 1–50 (2015) ´ B´enyi, K. Okoudjou, Local well-posedness of nonlinear dispersive equations on modulation 4. A. spaces. Bull. Lond. Math. Soc. 41(3), 549–558 (2009) 5. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schr¨odinger equations. Geom. Funct. Anal. 3, 107–156 (1993) 6.

Then, 2-nilpotent bridging is the best possible case from the point of view of simplicity of computations. (2) Cardinal spectral reduction is another case of spectral bridging. The goal of this method is to decrease the number of nonzero eigenvalues of the reduced error operator. When we choose a bridge set with smaller than optimal cardinality, cardinal spectral reduction occurs naturally. (3) Radial spectral reduction is the last case of spectral bridging. Here the goal is to reduce the spectral radius of the reduced error operator (cf.

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