Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Annalen"
DOI: 10.1007/s00208-021-02156-z
Abstract: We prove sharp estimates for Fourier transforms of indicator functions of bounded open sets in $${\mathbb {R}}^n$$ R n with real analytic boundary, as well as nontrivial lattice point discrepancy results. Both are derived from… read more here.
Keywords: fourier transforms; lattice point; point discrepancy; stability ... See more keywords
Fourier transforms on finite group actions and bent functions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Algebraic Combinatorics"
DOI: 10.1007/s10801-021-01057-3
Abstract: Highly nonlinear functions (bent functions, perfect nonlinear functions, etc.) on finite fields and finite (abelian or nonabelian) groups have been studied in numerous papers. As a generalization of bent functions on finite groups, bent functions… read more here.
Keywords: group; bent functions; functions finite; complex valued ... See more keywords
Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations
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DOI: 10.1007/s11425-015-9029-0
Abstract: We study solutions to convolution equations for functions with discrete support in ℝn, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a… read more here.
Keywords: transforms solutions; convolution equations; convolution; domains holomorphy ... See more keywords
Quantification of relative neurite tortuosity using Fourier transforms
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Neuroscience Methods"
DOI: 10.1016/j.jneumeth.2021.109266
Abstract: BACKGROUND The tortuosity of nerve fibers has been shown to be important for identifying and monitoring clinically relevant manifestations resulting from of a variety of ocular and systemic disease pathologies and disorders. However, quantifying tortuosity… read more here.
Keywords: neurite tortuosity; require manual; tortuosity; methods require ... See more keywords
Fourier transforms for fast and quantitative Laser Speckle Imaging
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DOI: 10.1038/s41598-019-49570-7
Abstract: Laser speckle imaging is a powerful imaging technique that visualizes microscopic motion within turbid materials. At current two methods are widely used to analyze speckle data: one is fast but qualitative, the other quantitative but… read more here.
Keywords: fast quantitative; speckle; laser speckle; speckle imaging ... See more keywords
Optimized Nonuniform FFTs and Their Application to Array Factor Computation
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Transactions on Antennas and Propagation"
DOI: 10.1109/tap.2018.2826368
Abstract: We deal with developing an optimized approach for implementing nonuniform fast Fourier transform (NUFFT) algorithms under a general and new perspective for 1-D transformations. The computations of nonequispaced results, nonequispaced data, and Type-3 nonuniform discrete… read more here.
Keywords: fourier transforms; ffts application; nonuniform ffts; computation ... See more keywords
Irregularity-Aware Graph Fourier Transforms
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Signal Processing"
DOI: 10.1109/tsp.2018.2870386
Abstract: In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs.… read more here.
Keywords: graph fourier; graph; aware graph; irregularity aware ... See more keywords
On Some Topological Properties of Fourier Transforms of Regular Holonomic ${\mathcal{D}}$-Modules
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DOI: 10.4153/s0008439519000559
Abstract: Abstract We study Fourier transforms of regular holonomic ${\mathcal{D}}$-modules. In particular, we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic ${\mathcal{D}}$-modules will be given. Moreover, we give… read more here.
Keywords: holonomic mathcal; fourier transforms; topological properties; mathcal modules ... See more keywords