Zobrazeno 1 - 10
of 277
pro vyhledávání: '"Seip, Kristian"'
We study the function $\varphi_1$ of minimal $L^1$ norm among all functions $f$ of exponential type at most $\pi$ for which $f(0)=1$. This function, first studied by H\"{o}rmander and Bernhardsson in 1993, has only real zeros $\pm \tau_n$, $n=1,2, \l
Externí odkaz:
http://arxiv.org/abs/2407.00970
Let $\mathfrak{p}_d(q)$ denote the critical exponent of the Riesz projection from $L^q(\mathbb{T}^d)$ to the Hardy space $H^p(\mathbb{T}^d)$, where $\mathbb{T}$ is the unit circle. We present the state-of-the-art on the conjecture that $\mathfrak{p}_
Externí odkaz:
http://arxiv.org/abs/2402.09787
Autor:
Brevig, Ole Fredrik, Seip, Kristian
Publikováno v:
Pure Appl. Funct. Anal. 9 (2024), no. 4, 991--994
We show that the norm of the backward shift operator on $H^1$ is $2/\sqrt{3}$, and we identify the functions for which the norm is attained.
Comment: This paper has been accepted for publication in Pure and Applied Functional Analysis
Comment: This paper has been accepted for publication in Pure and Applied Functional Analysis
Externí odkaz:
http://arxiv.org/abs/2309.11360
Publikováno v:
Bull. London Math. Soc. 55 (2023), 2963-2975
We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large values of Dirichlet $L$-fun
Externí odkaz:
http://arxiv.org/abs/2302.08285
Autor:
Brevig, Ole Fredrik, Seip, Kristian
Publikováno v:
J. Math. Anal. Appl. 529 (2024), no. 2, 127221
A Hankel operator $\mathbf{H}_\varphi$ on the Hardy space $H^2$ of the unit circle with analytic symbol $\varphi$ has minimal norm if $\|\mathbf{H}_\varphi\|=\|\varphi \|_2$ and maximal norm if $\|\mathbf{H}_\varphi\| = \|\varphi\|_\infty$. The Hanke
Externí odkaz:
http://arxiv.org/abs/2301.07937
Publikováno v:
J. Anal. Math. 153 (2024), no. 2, 595--670
We study the norm of point evaluation at the origin in the Paley--Wiener space $PW^p$ for $0 < p < \infty$, i. e., we search for the smallest positive constant $C$, called $\mathscr{C}_p$, such that the inequality $|f(0)|^p \leq C \|f\|_p^p$ holds fo
Externí odkaz:
http://arxiv.org/abs/2210.13922
Publikováno v:
Algebra i Analiz 34 (2022), no. 3, 131--158 or St. Petersburg Math. J. 34 (2023), no. 3, 405--425
A Hilbert point in $H^p(\mathbb{T}^d)$, for $d\geq1$ and $1\leq p \leq \infty$, is a nontrivial function $\varphi$ in $H^p(\mathbb{T}^d)$ such that $\| \varphi \|_{H^p(\mathbb{T}^d)} \leq \|\varphi + f\|_{H^p(\mathbb{T}^d)}$ whenever $f$ is in $H^p(\
Externí odkaz:
http://arxiv.org/abs/2106.07532
Publikováno v:
Geom. Funct. Anal. 31 (2021), no. 6, 1377--1413
We describe the idempotent Fourier multipliers that act contractively on $H^p$ spaces of the $d$-dimensional torus $\mathbb{T}^d$ for $d\geq 1$ and $1\leq p \leq \infty$. When $p$ is not an even integer, such multipliers are just restrictions of cont
Externí odkaz:
http://arxiv.org/abs/2103.16186
Autor:
Brevig, Ole Fredrik, Seip, Kristian
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2024 529(2)
