The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Aaron Pollack - One of the best experts on this subject based on the ideXlab platform.
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a g 2 period of a Fourier Coefficient of an eisenstein series on e 6
Israel Journal of Mathematics, 2019Co-Authors: Aaron Pollack, Chen Wan, Michal ZydorAbstract:We calculate a G2-period of a Fourier Coefficient of a cuspidal Eisenstein series on the split simply-connected group E6, and relate this period to the Ginzburg-Rallis period of cusp forms on GL6. This gives us a relation between the Ginzburg-Rallis period and the central value of the exterior cube L-function of GL6.
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a mathrm g _2 period of a Fourier Coefficient of an eisenstein series on mathrm e _6
arXiv: Number Theory, 2018Co-Authors: Aaron Pollack, Chen Wan, Michal ZydorAbstract:We calculate a $\mathrm{G}_2$-period of a Fourier Coefficient of a cuspidal Eisenstein series on the split simply-connected group $\mathrm{E}_6$, and relate this period to the Ginzburg-Rallis period of cusp forms on $\mathrm{GL}_6$. This gives us a relation between the Ginzburg-Rallis period and the central value of the exterior cube L-function of $\mathrm{GL}_6$
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The spin -function on for Siegel modular forms
Compositio Mathematica, 2017Co-Authors: Aaron PollackAbstract:We give a Rankin-Selberg integral representation for the Spin (degree eight) $L$-function on $\mathrm{PGSp}_6$. The integral applies to the cuspidal automorphic representations associated to Siegel modular forms. If $\pi$ corresponds to a level one Siegel modular form $f$ of even weight, and if $f$ has a non-vanishing maximal Fourier Coefficient (defined below), then we deduce the functional equation and finiteness of poles of the completed Spin $L$-function $\Lambda(\pi,Spin,s)$ of $\pi$.
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The spin -function on for Siegel modular forms
Compositio Mathematica, 2017Co-Authors: Aaron PollackAbstract:We give a Rankin–Selberg integral representation for the Spin (degree eight) $L$-function on $\operatorname{PGSp}_{6}$ that applies to the cuspidal automorphic representations associated to Siegel modular forms. If $\unicode[STIX]{x1D70B}$ corresponds to a level-one Siegel modular form $f$ of even weight, and if $f$ has a nonvanishing maximal Fourier Coefficient (defined below), then we deduce the functional equation and finiteness of poles of the completed Spin $L$-function $\unicode[STIX]{x1D6EC}(\unicode[STIX]{x1D70B},\text{Spin},s)$ of $\unicode[STIX]{x1D70B}$.
Yujiao Jiang - One of the best experts on this subject based on the ideXlab platform.
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On sums of Fourier Coefficients of Maass cusp forms
International Journal of Number Theory, 2017Co-Authors: Yujiao JiangAbstract:Let ϕ be a Hecke–Maass cusp form, and aϕ(n) be its nth Fourier Coefficient at the cusp infinity. In this paper, we are interested in the estimation on sums ∑n≤xaϕ(nj) for 1 ≤ j ≤ 4. We are able to improve previous results by introducing some inequalities concerning Fourier Coefficients and other techniques.
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On sums of Fourier Coefficients of Maass cusp forms
International Journal of Number Theory, 2017Co-Authors: Yujiao JiangAbstract:Let [Formula: see text] be a Hecke–Maass cusp form, and [Formula: see text] be its [Formula: see text]th Fourier Coefficient at the cusp infinity. In this paper, we are interested in the estimation on sums [Formula: see text] for [Formula: see text] We are able to improve previous results by introducing some inequalities concerning Fourier Coefficients and other techniques.
Narendra Ahuja - One of the best experts on this subject based on the ideXlab platform.
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vision based fire detection
International Conference on Pattern Recognition, 2004Co-Authors: Narendra AhujaAbstract:Vision based fire detection is potentially a useful technique. With the increase in the number of surveillance cameras being installed, a vision based fire detection capability can be incorporated in existing surveillance systems at relatively low additional cost. Vision based fire detection offers advantages over the traditional methods. It will thus complement the existing devices. In this paper, we present spectral, spatial and temporal models of fire regions in visual image sequences. The spectral model is represented in terms of the color probability density of fire pixels. The spatial model captures the spatial structure within a fire region. The shape of a fire region is represented in terms of the spatial frequency content of the region contour using its Fourier Coefficients. The temporal changes in these Coefficients are used as the temporal signatures of the fire region. Specifically, an auto regressive model of the Fourier Coefficient series is used. Experiments with a large number of scenes show that our method is capable of detecting fire reliably.
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ICPR (4) - Vision based fire detection
2004Co-Authors: Narendra AhujaAbstract:Vision based fire detection is potentially a useful technique. With the increase in the number of surveillance cameras being installed, a vision based fire detection capability can be incorporated in existing surveillance systems at relatively low additional cost. Vision based fire detection offers advantages over the traditional methods. It will thus complement the existing devices. In this paper, we present spectral, spatial and temporal models of fire regions in visual image sequences. The spectral model is represented in terms of the color probability density of fire pixels. The spatial model captures the spatial structure within a fire region. The shape of a fire region is represented in terms of the spatial frequency content of the region contour using its Fourier Coefficients. The temporal changes in these Coefficients are used as the temporal signatures of the fire region. Specifically, an auto regressive model of the Fourier Coefficient series is used. Experiments with a large number of scenes show that our method is capable of detecting fire reliably.
Shigeyoshi Ogawa - One of the best experts on this subject based on the ideXlab platform.
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on a stochastic Fourier Coefficient case of noncausal functions
Journal of Theoretical Probability, 2014Co-Authors: Shigeyoshi Ogawa, Hideaki UemuraAbstract:Given a random function \(f(t,\omega )\) and an orthonormal basis \(\{\varphi _n \}\) in \(L^2(0,1),\) we are concerned with the basic question whether the function can be reconstructed from the complete set of its stochastic Fourier Coefficients \(\{{\hat{f}}_n(\omega )\}\) which are defined by the following stochastic integral with respect to the Brownian motion \(W.\): \({\hat{f}}_n(\omega ):=\int _0^1 f(t,\omega ) \overline{\varphi _n(t)}{\text{ d}}_*W_t\), where the symbol \(\int {\text{ d}}_*W_t\) stands for the stochastic integral of noncausal type. In an earlier article (Stochastics, doi: 10.1080/17442508.2011.651621, 2012), Ogawa studied the question in the limited framework of homogeneous chaos and gave some affirmative answers when the random functions are causal and square integrable Wiener functionals for which the Ito integral is used for the definition of the stochastic Fourier Coefficient. In this note, we aim to extend those results to the more general case where the functions are free from the causality restriction and the Skorokhod integral is employed instead of the Ito integral.
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on a stochastic Fourier transformation
Stochastics An International Journal of Probability and Stochastic Processes, 2013Co-Authors: Shigeyoshi OgawaAbstract:Given a random function and an orthonormal basis in the , we are concerned with the basic properties of its stochastic Fourier Coefficient (SFC) which is defined by the stochastic integral with respect to the Brownian motion, . More precisely we are concerned in this note with the problem of reconstructing the function from its SFCs. We will show as our main result the affirmative answer when the random function belongs to a certain restricted but wide enough subclass, which is the class of causal Wiener functionals.
Hideaki Uemura - One of the best experts on this subject based on the ideXlab platform.
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on a stochastic Fourier Coefficient case of noncausal functions
Journal of Theoretical Probability, 2014Co-Authors: Shigeyoshi Ogawa, Hideaki UemuraAbstract:Given a random function \(f(t,\omega )\) and an orthonormal basis \(\{\varphi _n \}\) in \(L^2(0,1),\) we are concerned with the basic question whether the function can be reconstructed from the complete set of its stochastic Fourier Coefficients \(\{{\hat{f}}_n(\omega )\}\) which are defined by the following stochastic integral with respect to the Brownian motion \(W.\): \({\hat{f}}_n(\omega ):=\int _0^1 f(t,\omega ) \overline{\varphi _n(t)}{\text{ d}}_*W_t\), where the symbol \(\int {\text{ d}}_*W_t\) stands for the stochastic integral of noncausal type. In an earlier article (Stochastics, doi: 10.1080/17442508.2011.651621, 2012), Ogawa studied the question in the limited framework of homogeneous chaos and gave some affirmative answers when the random functions are causal and square integrable Wiener functionals for which the Ito integral is used for the definition of the stochastic Fourier Coefficient. In this note, we aim to extend those results to the more general case where the functions are free from the causality restriction and the Skorokhod integral is employed instead of the Ito integral.