Quasi-spectral decomposition of the heat potential

• Main Authors: Tynysbek Sh. Kal'menov, Gaukhar D. Arepova
• Format: Article
• Language: English
• Published: Texas State University 2016-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Heat potential; quasi-spectral decomposition; self-adjoint operator; unitary operator; the fundamental solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/76/abstr.html

In this article, by multiplying of the unitary operator $$ (Pf)(x,t)=f(x,T-t),\quad 0\leq t\leq T, $$ the heat potential turns into a self-adjoint operator. From the spectral decomposition of this completely continuous self-adjoint operator we obtain a quasi-spectral decomposition of the heat potential operator.