Uniform estimates for Fourier restriction to polynomial curves in ℝd

2016 ◽  
Vol 138 (2) ◽  
pp. 449-471 ◽  
Author(s):  
Betsy Stovall
Keyword(s):  
Uniform Estimates ◽  
Polynomial Curves ◽  
Fourier Restriction

scholarly journals Fourier restriction to polynomial curves I: a geometric inequality

2010 ◽  
Vol 132 (4) ◽  
pp. 1031-1076 ◽  
Author(s):  
Spyridon Dendrinos ◽  
James Wright
Keyword(s):  
Geometric Inequality ◽  
Polynomial Curves ◽  
Fourier Restriction

scholarly journals Uniform estimates for the X-ray transform restricted to polynomial curves

2012 ◽  
Vol 262 (12) ◽  
pp. 4986-5020 ◽  
Author(s):  
Spyridon Dendrinos ◽  
Betsy Stovall
Keyword(s):  
X Ray ◽  
Ray Transform ◽  
Uniform Estimates ◽  
Polynomial Curves

scholarly journals Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

2021 ◽  
Vol 182 (2) ◽  
Author(s):  
Li Chen ◽  
Jinyeop Lee ◽  
Matthew Liew
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Weak Limit ◽  
Weak Compactness ◽  
Three Dimensions ◽  
Uniform Estimates ◽  
Fermionic Systems ◽  
Semiclassical Limits ◽  
Semiclassical Regime

AbstractWe study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$\hbar = N^{-1/3}$$ ħ = N - 1 / 3 in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

2021 ◽  
pp. 1-29
Author(s):  
ALEXANDER BRUDNYI
Keyword(s):  
Disjoint Union ◽  
A Priori ◽  
Holomorphic Functions ◽  
Stable Rank ◽  
Open Unit ◽  
Uniform Estimates ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Similar Approximation ◽  
Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

Uniform Estimates on the Tsallis Entropies

2007 ◽  
Vol 80 (2) ◽  
pp. 171-181 ◽  
Author(s):  
Zhengmin Zhang
Keyword(s):  
Uniform Estimates

scholarly journals Uniform Estimates of Nonlinear Spectral Gaps

2014 ◽  
Vol 31 (5) ◽  
pp. 1517-1530
Author(s):  
Takefumi Kondo ◽  
Tetsu Toyoda
Keyword(s):  
Spectral Gaps ◽  
Uniform Estimates
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