1,721,250 research outputs found
Anh Bui
No full textAnh Bui, second place winner, presents his research.https://thekeep.eiu.edu/lib_awards_2024_photos/1009/thumbnail.jp
Anh Bui
No full textAnh Bui (Business and Technology) presents his paper Hempcrete Curtain Wallshttps://thekeep.eiu.edu/lib_awards_2024_video/1000/thumbnail.jp
(L-R) Lynne Cameron (BCAC Chair), Anh Bui, Brian Keith (Dean of Library Services)
No full textAnh Bui receives second place in the graduate category.https://thekeep.eiu.edu/lib_awards_2024_photos/1008/thumbnail.jp
Interview with Anh Bui, Executive Publication Manager, Books Products, High Wire Press
No full textThis interview is with Anh Bui, Executive Publication Manager, Books Products, High Wire Press, and discusses services provided by the company
Generalized Hardy Operators
Get PDFConsider the operator on
\begin{equation*}%\label{defn-La}
\La = (-\Delta)^{\alpha/2}+a|x|^{-\alpha} \quad \text{with} \quad 0<\alpha<\min\{2, d\}.
\end{equation*}
Under the condition
a\ge -\f{2^\alpha\Gamma((d+\alpha)/4)^2}
{\Gamma((d-\alpha)/4)^2}
the operator is non negative and selfadjoint.
We prove that fractional powers
for satisfy the estimates
\begin{equation*}
\|\mathcal{L}_{a}^{s/2}f\|_{L^{p}}
\lesssim\|(-\Delta)^{s/2}f\|_{L^{p}},
\qquad
\|(-\Delta)^{s/2}f\|_{L^{p}}
\lesssim \|\mathcal{L}_{a}^{s/2}f\|_{L^{p}}
\end{equation*}
for suitable ranges of . Our result fills the remaining gap
in earlier results from \cite{K.et.al}, \cite{FMS}, \cite{Merz}.
The method of proof is based on square function estimates for
operators whose heat kernel has a weak decay
Sharp L^p estimates for Schrödinger groups on spaces of homogeneous type
Get PDFWe prove an L^p estimate for the Schrodinger group e^{-itL}
generated by a semibounded, selfadjoint operator L on a metric measure space
X of homogeneous type. The assumptions on L are a mild L^{p_0} to L^{p_0}'
smoothing estimate and a mild L^2 to L^2 off--diagonal estimate for the
corresponding heat kernel e^{-tL}
sj-docx-1-apy-10.1177_10398562211037335 – Supplemental material for Stocktake of <i>Australasian Psychiatry’s</i> training resources
No full textSupplemental material, sj-docx-1-apy-10.1177_10398562211037335 for Stocktake of Australasian Psychiatry’s training resources by Michael Weightman, Tuan Anh Bui and Oliver D’Arcy Robertson in Australasian Psychiatry</p
On sharp estimates for Schrödinger groups of fractional powers of nonnegative self-adjoint operators
Get PDFLet be a non negative, selfadjoint operator on ,
where is a metric space endowed with a doubling measure.
Consider the Schr\"{o}dinger group for fractional powers
of . If the heat flow
satisfies suitable conditions of Davies--Gaffney
type, we obtain the following estimate in Hardy spaces
associated to :
\begin{equation*}
\big\|(I+L)^{-\beta /2}e^{i\tau L^{\gamma /2}}f\big\|_{H^p_L(X)}
\leq C (1 + |\tau|)^{n\mathfrak s_p}\|f\|_{H^p_L(X)}
\end{equation*}
where ,
,
and .
If in addition
satisfies a localized
polynomial estimate for some , we obtain
\begin{equation*}
\big\|(I+L)^{-\beta /2}e^{i\tau L^{\gamma /2}}f\big\|_{p_0,\vc}
\leq C (1 + |\tau|)^{n\mathfrak s_{p_0}}\|f\|_{p_0},
\quad \forall \tau \in \mathbb{R}.
\end{equation*}
provided
0<\gamma \ne 1,
and . By interpolation, the second estimate
implies also, for all , the strong
type estimate
\begin{equation*}
\big\|(I+L)^{-\beta /2}e^{i\tau L^{\gamma /2}}f\big\|_{p}
\leq C (1 + |\tau|)^{n\mathfrak s_{p_0}}\|f\|_{p}.
\end{equation*
On the flows associated to selfadjoint operators on metric measure spaces
Get PDFLet X be a metric space with a doubling measure satisfying μ(B)≳rBn for any ball B with any radius rB> 0. Let L be a non negative selfadjoint operator on L2(X). We assume that e-tL satisfies a Gaussian upper bound and that the flow eitL satisfies a typical L1- L∞ dispersive estimate of the form
‖eitL‖L1→L∞≲|t|-n/2.
Then we prove a similar L1- L∞ dispersive estimate for a general class of flows eitφ(L), with φ(r) of power type near 0 and near ∞. In the case of fractional powers φ(L) = Lν, ν∈ (0 , 1) , we deduce dispersive estimates for eitLν with data in Sobolev, Besov or Hardy spaces HLp with p∈ (0 , 1] , associated to the operator L
Introducing trainee editors and The Thought Broadcast podcast: Stepping forward for trainee research
No full textTrainee EditorialMichael Weightman, Tuan Anh Bui, Oliver D’Arcy Robertso
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