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TMF, 2013, Volume 174, Number 2, Pages 208–215 (Mi tmf8390)  

Nonexistence of solutions of the $p$-adic strings

V. S. Vladimirov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: We discuss mathematical aspects of the nonexistence of continuous (nontrivial) solutions of boundary value problems for equations of $p$-adic closed and open strings in the one-dimensional case. We find that the number of sign changes of the solution $\psi(t)$ is not equal to the order of zeros of the function $\psi^n(t)$ and that nonnegative (nonpositive) solutions do not exist. In the case of even $n$, if a solution $\psi$ exists, then the orders of zeros of the function $\psi^n$ and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form $2(2r+1)$, $r\ge0$.

Keywords: $p$-adic string, tachyon, pseudodifferential operator

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-2928.2012.1
Russian Foundation for Basic Research 11-01-00828_a


DOI: https://doi.org/10.4213/tmf8390

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English version:
Theoretical and Mathematical Physics, 2013, 174:2, 178–185

Bibliographic databases:

Document Type: Article
Received: 28.06.2012

Citation: V. S. Vladimirov, “Nonexistence of solutions of the $p$-adic strings”, TMF, 174:2 (2013), 208–215; Theoret. and Math. Phys., 174:2 (2013), 178–185

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