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