Applied philosophy in mathematics

Автор(и)

  • Yuri Kondratiev Bielefeld University, Germany and Dragomanov University, Kyiv

DOI:

https://doi.org/10.31392/iscs.2020.16.033

Ключові слова:

discrete measures, configuration spaces, reflection maps

Анотація

We show a possibility to apply certain philosophical concepts
to the analysis of concrete mathematical structures. Such application gives
a clear justification of topological and geometric properties of considered
mathematical objects.

Посилання

S. Albeverio, Y. G. Kondratiev, E.W. Lytvynov, and G. F. Us. 2006. Analysis and geometry on marked configuration spaces. arXiv Mathematics e-prints, math/0608344.

S. Albeverio, Yu. G. Kondratiev, and M. RoЁckner. 1998. Analysis and geometry on configuration spaces. J. Funct. Anal., 154(2):444–500.

A. Daletskii, Y. G. Kondratiev, and Y. Kozitsky. 2015. Phase transitions in continuum ferromagnets with unbounded spins. J. Math. Phys., 56(11):113502, 16. [4] D.Finkelshtein, Y.Kondratiev, P.Kuchling, and M.J.Olivera. 2020. Analysis and geometry on the cone of discrete Radon measures I. Methods Funct. Anal. Topology (to appear).

D.Finkelshtein, Y.Kondratiev, P.Kuchling, and M.J.Olivera. 2020. Analysis and geometry on the cone of discrete Radon measures II. Methods Funct. Anal. Topology. (to appear).

I. M. Gelfand, M. I. Graev, and A. M. Vershik. 1985. Models of representations of current groups. In Representations of Lie groups and Lie algebras (Budapest, 1971), pages 121–179. Akad. Kiadoґ, Budapest.

D. Hagedorn, Y. G. Kondratiev, E. Lytvynov, and A. Vershik. 2016. Laplace operators in gamma analysis. In Stochastic and infinite dimensional analysis, Trends Math, pages 119–147. BirkhaЁuser/Springer, [Cham].

D. Hagedorn, Y. G. Kondratiev, T. Pasurek, and M. RoЁckner. 2013. Gibbs states over the cone of discrete measures. J. Funct. Anal., 264(11):2550–2583.

Y. G. Kondratiev and T. Kuna. 2002. Harmonic analysis on configuration space. I. General theory. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5(2):201–233.

Y. G. Kondratiev and O. Kutoviy. 2006. On the metrical properties of the configuration space. Math. Nachr., 279(7):774–783.

Y. G. Kondratiev, E. Lytvynov, and A. Vershik. 2015. Laplace operators on the cone of Radon measures. J. Funct. Anal., 269(9):2947–2976.

Y. G. Kondratiev, E. W. Lytvynov, and G. F. Us. 2006. Analysis and geometry on R+-marked configuration spaces. arXiv Mathematics e-prints, page math/0608347.

T. M. Liggett. 1985. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 276, Springer-Verlag, New York.

Yu. I. Manin. 1989, Reflections on arithmetic physics. In: Invariance and string theory Academic Press, pp. 293–303.

W. D. Ross. Plato’s theory of ideas. Clarendon Pr., Oxford, 1951.

H. Shimomura. Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms. J. Math. Kyoto Univ., 34(3):599–614, 1994.

A. Skorohod. Random processes with independent increments, volume 47 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the second Russian edition by P. V. Malyshev.

N. Tsilevich, A. Vershik, and M. Yor. An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. J. Funct. Anal., 185(1):274–296, 2001.

V. I. Vernadsky. Living Matter in the Biosphere, pages 56–60. Springer New York, New York, NY, 1998.

##submission.downloads##

Опубліковано

2020-05-23

Номер

Розділ

Математика. Філософські аспекти математики