ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Mathematical Colloquim

 

PROGRAM


ODELJENJE ZA MATEMATIKU

MATEMATIČKOG INSTITUTA SANU
                       OPŠTI MATEMATIČKI SEMINAR

NA MATEMATIČKOM FAKULTETU U BEOGRADU



PROGRAM ZA MART 2012.

 

NAPOMENA: Predavanja ce se odrzavati u Sali II na prvom spratu Matematickog instituta SANU, Knez-Mihailova 36 (zgrada preko puta SANU).

 

Petak, 02.03.2012. u 14h sala II MI
Professor Sandro Coriasco, Faculty of Mathematics, University of Torino

$L^P(R^n)$-BOUNDEDNESS OF ANISOTROPIC MULTIPLIERS AND OF $SG$ FOURIER INTEGRAL OPERATORS

Abstract: I will illustrate some recently obtained results about the continuity on $L^p(\mathbb{R}^n)$ of certain pseudodifferential and Fourier integral operators, defined through symbol classes satisfying global estimates on $\mathbb{R}^n$.

More precisely, I will first discuss necessary conditions for the $L^p(\mathbb{R}^n)$-continuity of multipliers $\sigma(D)$ associated with suitable, strictly positive, weight functions $\lambda,\psi=(\psi_1, \dots, \psi_n) \in\mathcal{C}(\mathbb{R}^n)$, $\lambda$ bounded. Namely, the derivatives of the symbol $\sigma$ satisfy, for all $\alpha\in\mathbb{Z}_+^n$ and suitable constants $C_{\alpha}\ge 0$, the `anisotropic estimates'' $$ |D^\alpha \sigma(\xi)|\le\lambda(\xi)\cdot \psi(\xi)^{-\alpha}, \quad \xi\in\mathbb{R}^n, $$ % where $\displaystyle\psi(\xi)^{-\alpha}=\prod_{j=1}^n \psi_j(\xi)^{-\alpha_j}$. This generalises a classical result by Beals, where no difference in the components of $\psi$ was allowed.

Subsequently, I will present an extension of a famous result by Seeger, Sogge and Stein, to the Fourier integral operators defined on $\mathbb{R}^n$ by means of the so-called $SG$-symbols (a class of symbols independently introduced in the '70s by Cordes and Parenti). The lack of compactness in the supports gives additional complications, which imply the need of controlling the behaviour at infinity of the involved amplitude and phase functions. An interesting aspect of the result is that this reflects in a corresponding `loss of decay at infinity'', completely analogous to the well-known `loss of smoothness''.

Petak, 23.03.2012. u 14h sala II, MI
Prof Miodrag Mateljević, Matematički fakultet, Beograd
PRIKAZ MONOGRAFIJA POD ZAJEDNIČKIM NASLOVOM "KONFORMNA, KVAZIKONFORMNA I HARMONIJSKA PRESLIKAVANJA"


Rukovodioci Odeljenja za matematiku Matematickog instituta SANU i Opsteg matematickog seminara na Matematickom fakultetu u Beogradu, Stevan Pilipovic i Sinisa Vrecica predlazu zajednicki program rada naucnih sastanaka.

Predavanja ce se odrzavati na Matematickom Institutu (sala 2), petkom sa pocetkom u 14 casova. Odeljenje za matematiku je opsti seminar sa najduzom tradicijom u Institutu.

Svakog meseca, jedno predavanje ce biti odrzano na Matematickom Fakultetu u terminu koji ce biti posebno odredjen.

Molimo sve zainteresovane ucesnike u radu naucnih sastanaka da posebno obrate paznju na vreme odrzavanja svakog sastanka. Na Matematickom fakultetu su moguce izmene termina.

Obavestenje o programu naucnih sastanaka ce biti objavljeno na oglasnim tablama MI (Beograd), MF (Beograd), PMF (Novi Sad), PMF (Nis) i PMF (Kragujevac).

Odeljenje za matematiku Matematickog instituta SANU

Stevan Pilipovic

Opsti matematicki seminar na Matematickom fakultetu u Beogradu,

Sinisa Vrecica


Ako zelite da se obavestenja o Vasim naucnim skupovima pojave u Newsletter of EMS (European Mathematical Society) i na Internetu na lokaciji EMS, onda se obratite na emsvesti@mi.sanu.ac.rs gde cete dobiti format obavestenja.