  神本 丈（かみもと じよう） データ更新日：2021.06.15 1 Joe Kamimoto, On Holomorphic Curves Tangent to Real Hypersurfaces of Infinite Type, The Journal of Geometric Analysis, https://doi.org/10.1007/s12220-020-00567-z, 2020.12, The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D’Angelo infinite type in Cn. In order to understand the situation of flatness of these hypersurfaces, it is natural to ask whether there exists a nonconstant holomorphic curve tangent to a given hypersurface to infinite order. A sufficient condition for this existence is given by using Newton polyhedra, which is an important concept in singularity theory. More precisely, equivalence conditions are given in the case of some model hypersurfaces.. 2 Joe Kamimoto, Toshihiro Nose, Meromorphy of local zeta functions in smooth model cases, Journal of Functional Analysis, 10.1016/j.jfa.2019.108408, 278, 6, 2020.04, [URL], It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general (C) smooth functions, the meromorphic extension problem is not obvious. Indeed, it has been recently shown that there exist specific smooth functions whose local zeta functions have singularities different from poles. In order to understand the situation of the meromorphic extension in the smooth case, we investigate a simple but essentially important case, in which the respective function is expressed as u(x,y)xayb+ flat function, where u(0,0)≠0 and a,b are nonnegative integers. After classifying flat functions into four types, we precisely investigate the meromorphic extension of local zeta functions in each case. Our results show new interesting phenomena in one of these cases. Actually, when a−1/a and their poles on the half-plane are contained in the set {−k/b:k∈Nwithk 0, mF ∈ ℤ + and m ∈ ℕ are determined by geometrical properties of the Newton polyhedron of defining functions of domains and the limit of Φ as ρ → 0 on Λ is a positive constant depending only on the Newton principal part of the defining function. Analogous results are obtained in the case of the Szegö kernel.. 20 Joe Kamimoto, Non-analytic Bergman and Szegö kernels for weakly pseudoconvex tube domains in ℂ2, Mathematische Zeitschrift, 10.1007/PL00004843, 236, 3, 585-603, 2001.01, [URL], For any weakly pseudoconvex tube domain in ℂ2 with real analytic boundary, there exist points on the boundary off the diagonal where the Bergman kernel and the Szegö kernel fail to be real analytic.. 21 Joe Kamimoto, Haseo Ki, Young One Kim, On the multiplicities of the zeros of laguerre-pólya functions, Proceedings of the American Mathematical Society, 128, 1, 189-194, 2000.12, We show that all the zeros of the Fourier transforms of the functions exp(-x2m), m = 1,2,⋯, are real and simple. Then, using this result, we show that there are infinitely many polynomials p(x1,⋯, xn) such that for each (m1,⋯, mn) ∈ (ℕ \ {0})n the translates of the function p(x1,⋯, xn)exp (-∑j=1nxj2mj) generate L1(ℝn). Finally, we discuss the problem of finding the minimum number of monomials pα(x1,⋯, xn), α ∈ A, which have the property that the translates of the functions pα(x1,⋯, xn)exp(-∑j=1nxj2mj), α ∈ A, generate L1ℝn), for a given (m1,⋯,mn) ∈ (ℕ\{0})n.. 22 Joe Kamimoto, The Bergman kernel on weakly pseudoconvex tube domains in C2, Proceedings of the Japan Academy Series A: Mathematical Sciences, 10.3792/pjaa.75.12, 75, 2, 12-15, 1999.01, [URL]. 23 Joe Kamimoto, On an integral of hardy and littlewood, Kyushu Journal of Mathematics, 10.2206/kyushujm.52.249, 52, 1, 249-263, 1998.01, [URL]. 24 Joe Kamimoto, On the non-analytic examples of christ and geller, Proceedings of the Japan Academy Series A: Mathematical Sciences, 10.3792/pjaa.72.51, 72, 3, 51-52, 1996.01, [URL]. ### 九大関連コンテンツ

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