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2016 | OriginalPaper | Buchkapitel

1.  p-Adic Analysis: Essential Ideas and Results

verfasst von : W. A. Zúñiga-Galindo

Erschienen in: Pseudodifferential Equations Over Non-Archimedean Spaces

Verlag: Springer International Publishing

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Abstract

In this chapter, we present, without proofs, the essential aspects and basic results on p-adic functional analysis needed in the book. For a detailed exposition on p-adic analysis the reader may consult [5, 105, 111].

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Nächstes Kapitel Parabolic-Type Equations and Markov Processes
Literatur
1.
Albeverio, S., Belopolskaya, Y.: Stochastic processes in \(\mathbb{Q}_{p}\) associated with systems of nonlinear PIDEs. p-Adic Numbers Ultrametric Anal. Appl. 1 (2), 105–117 (2009)
2.
Albeverio, S., Karwowski, W.: Diffusion in p-adic numbers. In: Ito, K., Hida, H. (eds.) Gaussian Random Fields, pp. 86–99. World Scientific, Singapore (1991)
3.
Albeverio, S., Karwowski, W.: A random walk on p-adics: the generator and its spectrum. Stoch. Process. Appl. 53, 1–22 (1994)MATHCrossRef
4.
Albeverio, S., Karwowski, W.: Jump processes on leaves of multibranching trees. J. Math. Phys. 49 (9), 093503, 20 pp. (2008)
5.
Albeverio, S., Khrennikov, A.Yu., Shelkovich, V.M.: Theory of p-Adic Distributions: Linear and Nonlinear Models. Cambridge University Press, Cambridge (2010)MATHCrossRef
6.
Ansari, A., Berendzen, J., Bowne, S.F., Frauenfelder, H., Iben, I.E.T., Sauke, T.B., Shyamsunder, E., Young, R.D.: Protein states and proteinquakes. Proc. Natl. Acad. Sci. USA 82, 5000–5004 (1985)CrossRef
7.
Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F.: Vector-Valued Laplace Transforms and Cauchy Problems. Birkhäuser-Springer, Basel (2011)MATHCrossRef
8.
Avetisov, V.A., Bikulov, A.H., Kozyrev, S.V.: Application of p-adic analysis to models of breaking of replica symmetry. J. Phys. A 32 (50), 8785–8791 (1999)MATHCrossRef
9.
Avetisov, V.A., Bikulov, A.Kh., Kozyrev, S.V.: Description of logarithmic relaxation by a model of a hierarchical random walk. Dokl. Akad. Nauk 368 (2), 164–167 (1999, in Russian)
10.
Avetisov, V.A., Bikulov, A.H., Kozyrev, S.V., Osipov, V.A.: p-Adic models of ultrametric diffusion constrained by hierarchical energy landscapes. J. Phys. A 35 (2), 177–189 (2002)
11.
Avetisov, V.A., Bikulov, A.Kh., Osipov, V.A.: p-Adic description of characteristic relaxation in complex systems. J. Phys. A 36 (15), 4239–4246 (2003)
12.
Avetisov, V.A., Bikulov, A.Kh., Osipov, V.A.: p-Adic models of ultrametric diffusion in the conformational dynamics of macromolecules. Proc. Steklov Inst. Math. 245 2, 48–57 (2004)
13.
Avetisov, V.A., Bikulov, A.Kh.: On the ultrametricity of the fluctuation dynamic mobility of protein molecules. Proc. Steklov Inst. Math. 265 (1), 75–81 (2009)MATHCrossRef
14.
Avetisov, V.A., Bikulov, A.Kh., Zubarev, A.P.: First passage time distribution and the number of returns for ultrametric random walks. J. Phys. A 42 (8), 085003, 18 pp. (2009)
15.
Atiyah, M.F.: Resolution of singularities and division of distributions. Commun. Pure Appl. Math. 23,145–150 (1970)MATHCrossRef
16.
Bass, R.F., Levin, D.A.: Transition probabilities for symmetric jump processes. Trans. Am. Math. Soc. 354 (7), 2933–2953 (2002)MATHCrossRef
17.
Berg, C., Forst, G.: Potential Theory on Locally Compact Abelian Groups. Springer, Berlin (1975)MATHCrossRef
18.
Bernstein, I.N.: Modules over the ring of differential operators; the study of fundamental solutions of equations with constant coefficients. Funct. Anal. Appl. 5 (2), 1–16 (1972)
19.
Beloshapka, O.: Feynman formulas for an infinite-dimensional p-adic heat type equation. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14 (1), 137–148 (2011)MATHCrossRef
20.
21.
Bikulov, A.Kh., Volovich, I.V.: p-Adic Brownian motion. Izv. Math. 61 (3), 537–552 (1997)
22.
Borevich, Z.I., Shafarevich, I.R.: Number Theory. Academic, London (1986)MATH
23.
Casas-Sánchez, O.F., Zúñiga-Galindo, W.A.: p-Adic elliptic quadratic forms, parabolic-type pseudodifferential equations with variable coefficients and Markov processes. p-Adic Numbers Ultrametric Anal. Appl. 6 (1), 1–20 (2014)
24.
Cazenave, T., Haraux, A.: An Introduction to Semilinear Evolution Equations. Oxford University Press, Oxford (1998)MATH
25.
Chacón-Cortes, L.F., Zúñiga-Galindo, W.A.: Nonlocal operators, parabolic-type equations, and ultrametric random walks. J. Math. Phys. 54, 113503 (2013) [Erratum 55, 109901 (2014)]
26.
Chacón-Cortes, L., Zúñiga-Galindo, W.A.: Non-local operators, non-Archimedean parabolic-type equations with variable coefficients and Markov processes. Publ. Res. Inst. Math. Sci. 51 (2), 289–317 (2015)MATHCrossRef
27.
Chacón-Cortes, L., Zúñiga-Galindo, W.A.: Heat traces and spectral zeta functions for p-adic laplacians. Accepted in Algebra i Analiz. arXiv:1511.02146
28.
Chen, Z.-Q., Kumagai, T.: Heat kernel estimates for jump processes of mixed types on metric measure spaces. Probab. Theory Relat. Fields 140 (1–2), 277–317 (2008)MATH
29.
Connes, A.: Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Sel. Math. (N.S.) 5, 29–106 (1999)
30.
31.
de Jager, E.M.: The Lorentz-invariant solutions of the Klein-Gordon equation. SIAM J. Appl. Math. 15, 944–963 (1967)MATHCrossRef
32.
de Jager, E.M.: Applications of Distributions in Mathematical Physics. Mathematical Centre Tracts, vol. 10. Mathematisch Centrum, Amsterdam (1964)
33.
Diamond, H.: Elementary methods in the study of the distribution of prime numbers. Bull. Am. Math. Soc. (N.S.) 7 (3), 553–589 (1982)
34.
Dimock, J.: Quantum Mechanics and Quantum Field Theory: A Mathematical Primer. Cambridge University Press, Cambridge (2011)MATHCrossRef
35.
Dragovich, B.: p-Adic and adelic quantum mechanics. Proc. Steklov Inst. Math. 245 (2), 64–77 (2004)
36.
Dragovich, B., Khrennikov, A.Yu., Kozyrev, S.V., Volovich, I.V.: On p-adic mathematical physics. p-Adic Numbers Ultrametric Anal. Appl. 1 (1), 1–17 (2009)
37.
Dragovich, B., Radyno, Y., Khrennikov, A.: Generalized functions on adeles. J. Math. Sci. (N.Y.) 142 (3), 2105–2112 (2007)
38.
Droniou, J., Gallouet, T., Vovelle, J.: Global solution and smoothing effect for a non-local regularization of a hyperbolic equation. J. Evol. Equ. 3 (3), 499–521 (2003)MATHCrossRef
39.
40.
Ehrenpreis, L.: Solution of some problems of division. Part I. Division by a polynomial of derivation. Am. J. Math. 76, 883–903 (1954)MATH
41.
Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Springer, New York (2000)MATH
42.
Evans, S.N.: Local properties of Lévy processes on a totally disconnected group. J. Theor. Probab. 2 (2), 209–259 (1989)MATHCrossRef
43.
44.
Folland, G.B.: Quantum Field Theory: A Tourist Guide for Mathematicians. American Mathematical Society, Providence (2008)MATHCrossRef
45.
Friedman, A.: Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs (1964)MATH
46.
Frauenfelder, H., McMahon, B.H., Fenimore, P.W.: Myoglobin, the hydrogen atom of biology and paradigm of complexity. Proc. Natl. Acad. Sci. USA 100 (15), 8615–8617 (2003)CrossRef
47.
Frauenfelder, H., Sligar, S.G., Wolynes, P.G.: The energy landscape and motions of proteins. Science 254, 1598–1603 (1991)CrossRef
48.
Galeano-Peñaloza, J., Zúñiga-Galindo, W.A.: Pseudo-differential operators with semi-quasielliptic symbols over p-adic fields: J. Math. Anal. Appl. 386 (1), 32–49 (2012)MATHCrossRef
49.
Gel’fand, I.M., Shilov, G.E.: Generalized Functions, vol. 1. Academic, New York (1977)MATH
50.
Goldfeld, D., Hundley, J.: Automorphic Representations and L-Functions for the General Linear Group, vol. I. Cambridge University Press, Cambridge (2011)MATHCrossRef
51.
Haran, S.: Potentials and explicit sums in arithmetic. Invent. Math. 101, 797–703 (1990)MATHCrossRef
52.
Haran, S.: Quantizations and symbolic calculus over the p-adic numbers. Ann. Inst. Fourier 43 (4), 997–1053 (1993)MATHCrossRef
53.
Harlow, D., Shenker, S., Stanford, D., Susskind, L.: Tree-like structure of eternal inflation: a solvable model. Phys. Rev. D 85 (6) (2012). Article Number: 063516
54.
Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. Math. 79, 109–326 (1964)MATHCrossRef
55.
Hörmander, L.: On the division of distributions by polynomials. Ark. Mat. 3, 555–568 (1958)MATHCrossRef
56.
Hörmander, L.: The Analysis of Linear Partial Differential Operators. II: Differential Operators with Constant Coefficients. Grundlehren der Mathematischen Wissenschaften, vol. 257. Springer, Berlin (1983)
57.
Igusa, J.-I.: An Introduction to the Theory of Local Zeta Functions. AMS/IP Studies in Advanced Mathematics, vol. 14. American Mathematical Society, Providence (2000)
58.
Igusa, J.-I.: Some aspects of the arithmetic theory of polynomials. Discrete Groups in Geometry and Analysis (New Haven, 1984). Progress in Mathematics, vol. 67, pp. 20–47. Birkhäuser, Boston (1987)
59.
Igusa, J.-I.: Zeta distributions associated with some invariants. Am. J. Math. 109 (1), 1–33 (1987)MATHCrossRef
60.
Jacob, N.: Pseudo Differential Operators and Markov Processes, Vol. II: Generators and Their Potential Theory, xxii+453 pp. Imperial College Press, London (2002)
61.
Karwowski, W.: Diffusion processes with ultrametric jumps. Rep. Math. Phys. 60 (2), 221–235 (2007)MATHCrossRef
62.
Karwowski, W., Mendes, R.V.: Hierarchical structures and asymmetric stochastic processes on p-adics and adèles. J. Math. Phys. 35 (9), 4637–4650 (1994)MATHCrossRef
63.
Kigami, J.: Transitions on a noncompact Cantor set and random walks on its defining tree. Ann. Inst. Henri Poincaré Probab. Stat. 49 (4), 1090–1129 (2013)MATHCrossRef
64.
Khrennikov, A.: p-Adic Valued Distributions in Mathematical Physics. Kluwer, Dordrecht (1994)
65.
Khrennikov, A.: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Kluwer, Dordrecht (1997)MATHCrossRef
66.
Khrennikov, A.Yu., Kozyrev, S.V.: Wavelets on ultrametric spaces. Appl. Comput. Harmon. Anal. 19, 61–76 (2005)MATHCrossRef
67.
Khrennikov, A.Yu., Kozyrev, S.V.: Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals. Phys. A: Stat. Mech. Appl. 359, 222–240 (2006)CrossRef
68.
Khrennikov, A.Yu., Kozyrev, S.V.: Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the $n ∖to0$ limit. Phys. A: Stat. Mech. Appl. 359, 241–266 (2006)CrossRef
69.
Khrennikov, A.Yu., Kozyrev, S.V.: Replica symmetry breaking related to a general ultrametric space III: the case of general measure. Phys. A: Stat. Mech. Appl. 378 (2), 283–298 (2007)CrossRef
70.
Khrennikov, A.Yu., Kozyrev, S.V.: Ultrametric random field. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9 (2), 199–213 (2006)MATHCrossRef
71.
Khrennikov, A.Yu., Kozyrev, S.V., Oleschko, K., Jaramillo, A.G., Correa, L.J.: Application of p-adic analysis to time series. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 16 (4), 1350030, 15 pp. (2013)
72.
Khrennikov, A.Y., Radyno, Y.V.: On adelic analogue of Laplacian. Proc. Jangjeon Math. Soc. 6 (1), 1–18 (2003)MATH
73.
Khrennikov, A.Y., Shelkovich, V.M., van der Walt, J.H.: Adelic multiresolution analysis, construction of wavelet bases and pseudo-differential operators. J. Fourier Anal. Appl. 19 (6), 1323–1358 (2013)MATHCrossRef
74.
Khrennikov, A.Yu., Kosyak, A.V., Shelkovich, V.M.: Wavelet analysis on adeles and pseudo-differential operators. J. Fourier Anal. Appl. 18 (6), 1215–1264 (2012)MATHCrossRef
75.
Khrennikov, A.Yu., Kozyrev, S.V.: Genetic code on the diadic plane. Phys. A: Stat. Mech. Appl. 381, 265–272 (2007)CrossRef
76.
Khrennikov, A.Yu., Kozyrev, S.V.: 2-Adic clustering of the PAM matrix. J. Theor. Biol. 261, 396–406 (2009)CrossRef
77.
Kozyrev, S.V., Khrennikov, A.Yu.: Pseudodifferential operators on ultrametric spaces, and ultrametric wavelets. Izv. Math. 69 (5), 989–1003 (2005)MATHCrossRef
78.
Khrennikov, A.Yu., Kozyrev, S.V.: p-Adic pseudodifferential operators and analytic continuation of replica matrices. Theor. Math. Phys. 144 (2), 1166–1170 (2005)
79.
80.
Kochubei, A.N.: Pseudo-Differential Equations and Stochastics over Non-Archimedean Fields. Marcel Dekker, New York (2001)MATHCrossRef
81.
Kochubei, A.N., Parabolic equations over the field of p-adic numbers. Math. USSR Izv. 39, 1263–1280 (1992)CrossRef
82.
Kozyrev, S.V.: Methods and applications of ultrametric and p-adic analysis: from wavelet theory to biophysics. Proc. Steklov Inst. Math. 274 (1 Suppl.), 1–84 (2011)MATHCrossRef
83.
Leichtnam, E.: Scaling group flow and Lefschetz trace formula for laminated spaces with p-adic transversal. Bull. Sci. Math. 131 (7), 638–669 (2007)MATHCrossRef
84.
Malgrange, B.: Existence et approximation des solutions des é quations aux dérivées partielles et des équations de convolution. Ann. Inst. Fourier 6, 271–355 (1955/1956)
85.
Manin, Y.I.: Reflections on Arithmetical Physics. Conformal Invariance and String Theory, pp. 293–303. Academic, New York (1989)
86.
Mézard, M., Parisi, G.: Virasoro Miguel Angel. Spin Glass Theory and Beyond. World Scientific, Singapore (1987)
87.
Ogielski, A.T., Stein, D.L.: Dynamics on ultrametric spaces. Phys. Rev. Lett. 55 (15), 1634–1637 (1985)CrossRef
88.
89.
Ortner, N., Wagner, P.: A short proof of the Malgrange-Ehrenpreis theorem. In: Dierolf, S., Dineen, S., Domański, P. (eds.) Functional Analysis. Proceedings of the 1st International Workshop in Trier, Germany, 1994, pp. 343–352. de Gruyter, Berlin (1996)
90.
Parisi, G., Sourlas N.: p-Adic numbers and replica symmetry breaking. Eur. Phys. J. B Condens. Matter Phys. 14 (3), 535–542 (2000)
91.
Radyno, Y.V., Radyna, Y.M.: Generalized Functions on Adeles. Linear and Non-linear Theories. Linear and Non-linear Theory of Generalized Functions and Its Applications. Banach Center Publications, vol. 88, pp. 243–250. Polish Academy of Sciences, Institute of Mathematics, Warsaw (2010)
92.
Rallis, S., Schiffmann, G.: Distributions invariantes par le groupe orthogonal. Analyse Harmonique Sur Les Groupes de Lie (Sém., Nancy-Strasbourg, 1973–1975). Lecture Notes in Mathematics, vol. 497, pp. 494–642. Springer, New York (1975)
93.
Ramakrishnan, D., Valenza, R.J.: Fourier Analysis on Number Fields. Springer, New York (1999)MATHCrossRef
94.
Rammal, R., Toulouse, G., Virasoro, M.A.: Ultrametricity for physicists. Rev. Mod. Phys. 58 (3), 765–788 (1986)CrossRef
95.
Reed, M., Simon, B.: Methods of Modern Mathematical Physics: Functional Analysis I. Academic, New York (1980)MATH
96.
Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. II: Fourier Analysis, Self-Adjointness. Academic, New York (1975)MATH
97.
Rodríguez-Vega, J.J.: On a general type of p-adic parabolic equations. Rev. Colomb. Mat. 43 (2), 101–114 (2009)MATH
98.
Rodríguez-Vega, J.J., Zúñiga-Galindo, W.A.: Taibleson operators, p-adic parabolic equations and ultrametric diffusion. Pac. J. Math. 237 (2), 327–347 (2008)MATHCrossRef
99.
Rosay, J.-P.: A very elementary proof of the Malgrange-Ehrenpreis theorem. Am. Math. Mon. 98 (6), 518–523 (1991)MATHCrossRef
100.
Rudin, W.: Fourier Analysis on Groups. Interscience, New York (1962)MATH
101.
Samko, S.G.: Hypersingular Integrals and Their Applications. Taylor and Francis, London (2002)MATH
102.
Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives and Some of Their Applications. Gordon and Breach Science Publishers, Yverdon (1993)MATH
103.
Schweber, S.S.: An Introduction to Relativistic Quantum Field Theory. Row/Peterson, Evanston (1961)MATH
104.
Serre, J.-P.: Lie Algebras and Lie Groups. American Mathematical Society, Providence (1968)
105.
Taibleson, M.H.: Fourier Analysis on Local Fields. Princeton University Press, Princeton (1975)MATH
106.
Torba, S.M., Zúñiga-Galindo, W.A.: Parabolic type equations and Markov stochastic processes on adeles. J. Fourier Anal. Appl. 19 (4), 792–835 (2013)MATHCrossRef
107.
Varadarajan, V.S.: Reflections on Quanta, Symmetries, and Supersymmetries. Springer, New York (2011)MATHCrossRef
108.
Varadarajan, V.S.: Path integrals for a class of p-adic Schr ödinger equations. Lett. Math. Phys. 39 (2), 97–106 (1997)MATHCrossRef
109.
Varadarajan, V.S.: Arithmetic quantum physics: why, what, and whither. Proc. Steklov Inst. Math. 245 (2), 258–265 (2004)MATH
110.
Veys, W., Zúñiga-Galindo, W.A.: Zeta functions for analytic mappings, log-principalization of ideals, and newton polyhedra. Trans. Am. Math. Soc. 360, 2205–2227 (2008)MATHCrossRef
111.
Vladimirov, V.S., Volovich, I.V., Zelenov, E.I.: p-Adic Analysis and Mathematical Physics. World Scientific, Singapore (1994)
112.
Volovich, I.V.: Number theory as the ultimate physical theory. p-Adic Numbers Ultrametric Anal. Appl. 2 (1), 77–87 (2010)
113.
Volovich, I.V.: p-Adic string. Class. Quantum Grav. 4, L83–L87 (1987)
114.
Wales, D.J., Miller, M.A., Walsh, T.R.: Archetypal energy landscapes. Nature 394, 758–760 (1998)CrossRef
115.
116.
Yasuda, K.: Markov processes on the adeles and representations of Euler products. J. Theor. Probab. 23 (3), 748–769 (2010)MATHCrossRef
117.
Zúñiga-Galindo, W.A.: Non-Archimedean white noise, pseudodifferential stochastic equations, and massive Euclidean fields. J. Fourier Anal. Appl. (2016). doi:10.1007/s00041-016-9470-1MATH
118.
Zúñiga-Galindo, W.A.: The non-Archimedean stochastic heat equation driven by Gaussian noise. J. Fourier Anal. Appl. 21 (3), 600–627 (2015)MATHCrossRef
119.
Zúñiga-Galindo, W.A.: The Cauchy problem for non-Archimedean pseudodifferential equations of Klein-Gordon type. J. Math. Anal. Appl. 420 (2), 1033–1050 (2014)MATHCrossRef
120.
Zúñiga-Galindo, W.A.: Local zeta functions and fundamental solutions for pseudo-differential operators over p-adic fields. p-Adic Numbers Ultrametric Anal. Appl. 3 (4), 344–358 (2011)
121.
Zúñiga-Galindo, W.A.: Local zeta functions supported on analytic sets and Newton polyhedra. Int. Math. Res. Not. IMRN (15), 2855–2898 (2009)MATH
122.
Zúñiga-Galindo, W.A.: Parabolic equations and Markov processes over p-adic fields. Potential Anal. 28 (2), 185–200 (2008)MATHCrossRef
123.
Zúñiga-Galindo, W.A.: Fundamental solutions of pseudo-differential operators over p-adic fields. Rend. Sem. Mat. Univ. Padova 109, 241–245 (2003)MATH
Metadaten
Titel
p-Adic Analysis: Essential Ideas and Results
verfasst von
W. A. Zúñiga-Galindo
Copyright-Jahr
2016
Buch
Pseudodifferential Equations Over Non-Archimedean Spaces

Print ISBN: 978-3-319-46737-5

Electronic ISBN: 978-3-319-46738-2

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-46738-2_1