Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Sahutoglu, Sonmez"'
Let $\varphi$ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator $C_{\varphi}$ is compact on the Bergman space if and only if $\varphi(\overline{\mathbb{D}^2})\cap \mathbb{T}^2=\emptyset$ a
Externí odkaz:
http://arxiv.org/abs/2409.09529
We study compactness of product of Toeplitz operators with symbols continuous on the closure of the polydisc in terms of behavior of the symbols on the boundary. For certain classes of symbols $f$ and $g$, we show that $T_fT_g$ is compact if and only
Externí odkaz:
http://arxiv.org/abs/2401.04869
Publikováno v:
Proc. Amer. Math. Soc. Ser. B 11 (2024), 406--421
Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^n$ with Lipschitz boundary and $\phi$ be a continuous function on $\overline{\Omega}$. We show that the Toeplitz operator $T_{\phi}$ with symbol $\phi$ is compact on the weighted Bergman sp
Externí odkaz:
http://arxiv.org/abs/2302.05013
We give sufficient conditions for the essential spectrum of the Hermitian square of a class of Hankel operators on the Bergman space of the polydisc to contain intervals. We also compute the spectrum in case the symbol is a monomial.
Comment: 17
Comment: 17
Externí odkaz:
http://arxiv.org/abs/2207.13116
Autor:
Sahutoglu, Sonmez
This dissertation consists of two parts. In the first part we show that for 1 k 1, a complex manifold M of dimension at least k in the boundary of a smooth bounded pseudoconvex domain in Cn is an obstruction to compactness of the @- Neumann operator
Externí odkaz:
http://hdl.handle.net/1969.1/3879
Autor:
Gogus, Nihat Gokhan, Sahutoglu, Sonmez
Publikováno v:
Complex Var. Elliptic Equ. 68 (2023), no. 8, 1419--1428
We prove that the Berezin transform is $L^p$ regular on a large class of domains in $\mathbb{C}^n$ and not $L^2$ regular on the Hartogs triangle.
Comment: A major revision. To appear in Complex Var. Elliptic Equ
Comment: A major revision. To appear in Complex Var. Elliptic Equ
Externí odkaz:
http://arxiv.org/abs/2108.07082
Publikováno v:
J. Operator Theory 89 (2023), no. 1, 75-85
Let $\Omega$ be a bounded convex domain in $\mathbb{C}^{n}$. We show that if $\varphi \in C^{1}(\overline{\Omega})$ is holomorphic along analytic varieties in $b\Omega$, then $H^{q}_{\varphi}$, the Hankel operator with symbol $\varphi$, is compact. W
Externí odkaz:
http://arxiv.org/abs/2011.02656
Autor:
Sahutoglu, Sonmez, Zeytuncu, Yunus E.
Publikováno v:
Bull. Lond. Math. Soc. 53, 2021, no. 5
Let $\Omega$ be a $C^4$-smooth bounded pseudoconvex domain in $\mathbb{C}^2$. We show that if the $\overline{\partial}$-Neumann operator $N_1$ is compact on $L^2_{(0,1)}(\Omega)$ then the embedding operator $\mathcal{J}:Dom(\overline{\partial})\cap D
Externí odkaz:
http://arxiv.org/abs/2009.13391
Publikováno v:
Can. Math. Bull. 65 (2022), no. 1, 170-179
Let $\Omega$ be a bounded Reinhardt domain in $\mathbb{C}^n$ and $\phi_1,\ldots,\phi_m$ be finite sums of bounded quasi-homogeneous functions. We show that if the product of Toeplitz operators $T_{\phi_m}\cdots T_{\phi_1}=0$ on the Bergman space on $
Externí odkaz:
http://arxiv.org/abs/2009.01951
Publikováno v:
Houston J. Math. 46 (2020), no. 4, 1005-1016
Let $\Omega$ be a bounded convex domain in $\mathbb{C}^{n}$, $n\geq 2$, $1\leq q\leq (n-1)$, and $\phi\in C(\bar{\Omega})$. If the Hankel operator $H^{q-1}_{\phi}$ on $(0,q-1)$--forms with symbol $\phi$ is compact, then $\phi$ is holomorphic along $q
Externí odkaz:
http://arxiv.org/abs/2005.14323