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
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 569-572
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 $p$.
@article{FPM_1995_1_2_a22,
author = {I. V. Tomina},
title = {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},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {569--572},
year = {1995},
volume = {1},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a22/}
}
TY - JOUR AU - I. V. Tomina TI - 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 JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 1995 SP - 569 EP - 572 VL - 1 IS - 2 UR - http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a22/ LA - ru ID - FPM_1995_1_2_a22 ER -
%0 Journal Article %A I. V. Tomina %T 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 %J Fundamentalʹnaâ i prikladnaâ matematika %D 1995 %P 569-572 %V 1 %N 2 %U http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a22/ %G ru %F FPM_1995_1_2_a22
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. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 569-572. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a22/
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