FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 2, PAGES 569-572

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

Consider the Hilbert space H = L2(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 $P\colon H\rightarrow H$ 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.

All articles are published in Russian.

Main page Editorial board
Instructions to authors Contents of the journal

Location: http://mech.math.msu.su/~fpm/eng/95/952/95223.htm
Last modified: October 3, 1997.