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Fundam. Prikl. Mat., 1995, Volume 1, Issue 2, Pages 569–572 (Mi fpm84)  

This article is cited in 1 scientific paper (total in 1 paper)

Short communications

The first regularized trace for a power of the Laplace operator on the rectangular triangle with the angle $\pi/6$ in case of Dirichlet problem

I. V. Tomina

Ivanovo State Power University

Abstract: Consider the Hilbert space $H=L^2(D)$, where $D=\{(x,y)\mid 0\leq y\sqrt{3}\leq x\leq(2\pi-y\sqrt{3})/3\}$. Let $T$ be the self-adjoint non-negative operator from $H$ to $H$ which is generated by the spectral Dirichlet problem $\Delta u+\lambda u=0$ on $D$, $u=0$ on $\partial D$. For $p\in L^\infty(D)$ let the operator $P\colon H\to H$ take each $f\in H$ to the product $p\cdot f$. In this paper concrete formulas for the first regularized trace of the operator $T^\alpha+P$, $\alpha>3/2$, are given for different classes of essentially bounded functions $p$.

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Bibliographic databases:
UDC: 517.95
Received: 01.01.1995

Citation: I. V. Tomina, “The first regularized trace for a power of the Laplace operator on the rectangular triangle with the angle $\pi/6$ in case of Dirichlet problem”, Fundam. Prikl. Mat., 1:2 (1995), 569–572

Citation in format AMSBIB
\Bibitem{Tom95}
\by I.~V.~Tomina
\paper The first regularized trace for a power of the Laplace operator on the rectangular triangle with the angle~$\pi/6$ in case of Dirichlet problem
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 2
\pages 569--572
\mathnet{http://mi.mathnet.ru/fpm84}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1790990}
\zmath{https://zbmath.org/?q=an:0866.35078}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. G. Tomin, “Several Formulas for the First Regularized Trace of Discrete Operators”, Math. Notes, 70:1 (2001), 97–109  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Фундаментальная и прикладная математика
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