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Non-archimedean functional analysis and its applications

Katagiri Yu 東北大学

2022.03.25

概要

In (usual) analysis, the fields R or C play a central role. For several reasons, people started to consider the implications of replacing R or C by the p-adic field Qp, or more generally, local fields. Because local fields are equipped with the “nonarchimedean” norm (i. e. the norm satisfies the “ultrametric triangle inequality”), the analysis over local fields is known as non-archimedean (also known as ultrametric or p-adic) analysis.

Let K be a local field, i.e., the quotient field of a complete discrete valuation ring R whose residue field κ has q elements. One equips K with the nonarchimedean norm | · | normalized so that |π| = q −1 for a uniformizer π of K. We define a K-Banach space to be a complete normed K-vector space B whose norm || · || satisfies the ultrametric triangle inequality ||v + w|| ≤ max{||v||, ||w||} for any v,w ∈ B. In this doctoral thesis, we mainly consider Banach spaces over local fields (especially, the Banach spaces of all continuous, continuously differentiable, or locally analytic functions). This thesis is organized as follows.

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参考文献

[1] Y. Amice, Interpolation p-adique, Bull. Soc. Math. France 92 (1964), 117-180.

[2] H. Ando and Y. Katagiri, A wavelet basis for non-Archimedean C n -functions and n-th Lipschitz functions, arXiv:2110.02486.

[3] T. Arakawa, T. Ibukiyama, and M. Kaneko, Bernoulli Numbers and Zeta Functions, Springer Monographs in Mathematics, Springer, Tokyo, 2014.

[4] T. Arakawa and M. Kaneko, Multiple zeta values, poly-Bernoulli numbers, and related zeta functions, Nagoya Math. J. 153 (1999), 189-209.

[5] L. Berger and C. Breuil, Sur quelques repr´esentations potentiellement cristallines de GL2(Qp), Asterisque ´ 330 (2010), 155–211.

[6] K. Bannai and S. Kobayashi, Integral structures on p-adic Fourier theory, Ann. Inst. Fourier (Grenoble) 66 (2016), no. 2, 521–550.

[7] P. Colmez, Le programme de Langlands p-adique, European Congress of Mathematics, Eur. Math. Soc., Zurich, 2013, pp. 259–284. ¨

[8] E. de Shalit, Mahler bases and elementary p-adic analysis, J. Theor. Nombres Bordeaux ´ 28 (2016), no. 3, 597–620.

[9] S. De Smedt, The van der Put base for C n -functions, Bull. Belg. Math. Soc. Simon Stevin 1 (1994), no. 1, 85–98.

[10] K. Imatomi, Multi-poly-Bernoulli-star numbers and finite multiple zeta-star values, Integers 14 (2014), Paper No. A51, 10.

[11] K. Imatomi, M. Kaneko, and E. Takeda, Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values, J. of Integer Seq. 17 (2014), 1-12.

[12] M. Kaneko, Poly-Bernoulli numbers, Journal de Theorie des Nombres de Bordeaux ´ 9 (1997), 199-206.

[13] Y. Katagiri, Kummer-type congruences for multi-poly-Bernoulli numbers, to appear in Commentarii Mathematici Universitatis Sancti Pauli.

[14] R. Kitahara, On Kummer-type congruences for poly-Bernoulli numbers (in Japanese), Tohoku University, master thesis (2012).

[15] K. Mahler, An interpolation series for continuous functions of a p-adic variable, J. Reine Angew. Math. 199 (1958), 23-34.

[16] E. Nagel, Partial fractional differentiability, Advances in ultrametric analysis, Contemp. Math., vol. 596, Amer. Math. Soc., Providence, RI, 2013, pp. 179–204.

[17] , p-adic Fourier theory of differentiable functions, Doc. Math. 23 (2018), 939–967.

[18] M. Sakata, On p-adic properties of poly-Bernoulli numbers (in Japanese), Kindai University, master thesis (2014).

[19] W. H. Schikhof, Ultrametric calculus, Cambridge Studies in Advanced Mathematics, vol. 4, Cambridge University Press, Cambridge, 1984.

[20] P. Schneider and J. Teitelbaum, p-adic Fourier theory, Doc. Math. 6 (2001), 447-481.

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