| Sharp Heat Kernel Estimates in the Fourier–Bessel Setting for a Continuous Range of the Type Parameter |
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| 基金项目： | supported by MNiSW(Grant No.N201 417839);supported by(Grant No.MTM2012-36732-C03-02)from Spanish Government |
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| 摘 要： | The heat kernel in the setting of classical Fourier–Bessel expansions is defined by an oscillatory series which cannot be computed explicitly.We prove qualitatively sharp estimates of this kernel.Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.Keywords Fourier–Bessel expansions,heat kernel,Bessel process,transition density
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| 关 键 词： | 内核 设置 傅里叶 类型 计数 塞尔 夏普 Jacobi |
Sharp heat kernel estimates in the Fourier-Bessel setting for a continuous range of the type parameter |
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| Authors: | Adam Nowak Luz Roncal |
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| Abstract: | The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an oscillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel. |
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| Keywords: | Fourier-Bessel expansions heat kernel Bessel process transition density |
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