**Seminar on Stohastics**

**PROGRAM**

Matematicki institut SANU

Kneza Mihaila 35/1

__PLAN RADA SEMINARA ZA JUN 2005.__

__Cetvrtak, 02. jun u 12 h.__

12h * Z. R. Pop-Stojanovic, Professor Emeritus, Department of Mathematics, University of Florida, Gainesville, Florida 32611, {zps@math.ufl.edu}: *

BROWNIAN POTENTIALS AND BESOV SPACES

15h * Z. R. Pop-Stojanovic: *

BROWNIAN POTENTIALS AND BESOV SPACES nastavak predavanja

__Cetvrtak, 09. jun u 12 h.__

12h * Z. R. Pop-Stojanovic: *

BROWNIAN POTENTIALS AND BESOV SPACES nastavak predavanja

15h *Z. R. Pop-Stojanovic: *

BROWNIAN POTENTIALS AND BESOV SPACES nastavak predavanja

These lectures will present results obtained jointly with M. Rao and H. Sikic in [*Brownian Potentials and Besov Spaces,* J. Math. Soc. Japan, Vol. **50**, No. **2**, (1958), 331-337], and later, concerning the c haracterization of Brownian Potentials in terms of a special type of interpolation spaces known as **Besov Spaces**. The main connection between these two concepts is based on the fact that Brownian potentials of finite measures given over bounded domains in $\rd$, belong to Besov Spaces. In the theory of function spaces, a class of spaces of distributions given on an Euclidean *n*-space, consists of Besov spaces $B_{pg}^{\al},$ where $\al\in\r, \; 0

0$ and $1\le p,q\le+\infty,$ these spaces were introduced in 1959 by O. V. Besov. [
*On a family of function spaces. Embedding theorems and extensions*,
**Dokl. Akad. Nauk. SSSR, (126)**, (1959), 1163--1165.] (However, the standard references on the subject are found in books by H. Triebel.[
*Theory of Function Spaces*, Birkh\"auser, Basel, 1983, and
*Theory of Function Spaces II*, Birkh\"auser, Basel, 1992.]). Using these spaces, it will be shown, among other things, that under some assumptions, the so-called
*gauge function*, which is a solution of the Schr\"odinger equation, belongs to the Besov space $\bpp (\Om),$ for $p

Slobodanka Jankovic i Svetlana Jankovic

rukovodioci seminara