scholarly journals On the restriction theorem for the paraboloid in ${\mathbb R}^4$

2019 ◽  
Vol 156 (2) ◽  
pp. 301-311
Author(s):  
Ciprian Demeter
Keyword(s):  
Restriction Theorem

SEMISTABILITY OF SYZYGY BUNDLES ON PROJECTIVE SPACES IN POSITIVE CHARACTERISTICS

2010 ◽  
Vol 21 (11) ◽  
pp. 1475-1504 ◽  
Author(s):  
V. TRIVEDI
Keyword(s):  
Line Bundle ◽  
Characteristic Zero ◽  
Projective Spaces ◽  
Restriction Theorem ◽  
Strong Restriction ◽  
Infinite Set

We generalize a result of Flenner, proved in characteristic zero, to positive characteristics. We prove that the first syzygy bundle, [Formula: see text], of the line bundle [Formula: see text] over [Formula: see text] is semistable, for a certain infinite set of integers d ≥ 0. Moreover, for arbitrary d, there is a "good enough estimate" on [Formula: see text] in terms of d and n; thus a strong restriction theorem of Langer, proved earlier for characteristic k > d, is valid in arbitrary characteristics.

scholarly journals NONCOMMUTATIVE DE LEEUW THEOREMS

2015 ◽  
Vol 3 ◽  
Author(s):  
MARTIJN CASPERS ◽  
JAVIER PARCET ◽  
MATHILDE PERRIN ◽  
ÉRIC RICARD
Keyword(s):  
Fourier Multiplier ◽  
Von Neumann Algebra ◽  
Modular Function ◽  
Discrete Subgroups ◽  
Original Proof ◽  
Restriction Theorem ◽  
Von Neumann ◽  
Lattice Approximation ◽  
Continuous Symbol ◽  
Group Von Neumann Algebra

Let $\text{H}$ be a subgroup of some locally compact group $\text{G}$. Assume that $\text{H}$ is approximable by discrete subgroups and that $\text{G}$ admits neighborhood bases which are almost invariant under conjugation by finite subsets of $\text{H}$. Let $m:\text{G}\rightarrow \mathbb{C}$ be a bounded continuous symbol giving rise to an $L_{p}$-bounded Fourier multiplier (not necessarily completely bounded) on the group von Neumann algebra of $\text{G}$ for some $1\leqslant p\leqslant \infty$. Then, $m_{\mid _{\text{H}}}$ yields an $L_{p}$-bounded Fourier multiplier on the group von Neumann algebra of $\text{H}$ provided that the modular function ${\rm\Delta}_{\text{G}}$ is equal to 1 over $\text{H}$. This is a noncommutative form of de Leeuw’s restriction theorem for a large class of pairs $(\text{G},\text{H})$. Our assumptions on $\text{H}$ are quite natural, and they recover the classical result. The main difference with de Leeuw’s original proof is that we replace dilations of Gaussians by other approximations of the identity for which certain new estimates on almost-multiplicative maps are crucial. Compactification via lattice approximation and periodization theorems are also investigated.

A Restriction Theorem for a k-Surface in ℝn

2005 ◽  
Vol 48 (2) ◽  
pp. 260-266 ◽  
Author(s):  
Daniel M. Oberlin
Keyword(s):  
Restriction Theorem ◽  
Fourier Restriction ◽  
Restriction Estimate

AbstractWe establish a sharp Fourier restriction estimate for a measure on a k-surface in ℝn, where n = k(k + 3)/2.

scholarly journals Chevalley's restriction theorem for reductive symmetric superpairs

2010 ◽  
Vol 323 (4) ◽  
pp. 1159-1185 ◽  
Author(s):  
Alexander Alldridge ◽  
Joachim Hilgert ◽  
Martin R. Zirnbauer
Keyword(s):  
Restriction Theorem

Some remarks on the restriction of the Fourier transform to surfaces

1993 ◽  
Vol 113 (1) ◽  
pp. 153-159 ◽  
Author(s):  
S. W. Drury ◽  
K. Guo
Keyword(s):  
Fourier Transform ◽  
Riesz Potential ◽  
Restriction Theorem ◽  
The Fourier Transform

AbstractFor a class of kernels, we prove the Lp estimate for the exotic Riesz potential, with which a restriction theorem of the Fourier transform to surfaces of half the ambient dimension is proved. A simpler proof of Barcelo's result is given. We also find that it is possible to combine the Hausdorff–Young theorem with the Fefferman–Zygmund method to prove some optimal results on the restriction theorem.

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