Gustavo Corach, Alejandra Maestripieri
A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.
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Sampling and Reconstruction in Different Subspaces by Using Oblique Projections
本文提出一种利用斜投影从线性测量中重建函数的新方法，通过不同子空间实现更优的近似常数。
Weighted Orlicz regularity for fully nonlinear elliptic equations with oblique derivative at the boundary via asymptotic operators
该研究针对带斜边界条件的完全非线性椭圆方程，在算子无需凸凹结构的条件下证明了加权Orlicz-Sobolev正则性，还处理了对应障碍问题的加权Orlicz估计，并给出Hessian的加权Orlicz-BMO正则性结果。
It is known that complementary oblique projections $\hat{P}_0 + \hat{P}_1 = I$ on a Hilbert space $\mathscr{H}$ have the same standard operator norm $\|\hat{P}_0\| = \|\hat{P}_1\|$ and the same singular values, but for the multiplicity of $0$ and $1$. We generalize these results to Hilbert spaces endowed with a positive-definite metric $G$ on top of the scalar product. Our main result is that the volume elements (pseudodeterminants $\det_+$) of the metrics $L_0,L_1$ induced by $G$ on the complementary oblique subspaces $\mathscr{H} = \mathscr{H}_0 \oplus \mathscr{H}_1$, and of those $\mathitΓ_…
Sampling and Reconstruction in Distinct Subspaces Using Oblique Projections
本文研究了在给定重建子空间上精确的重建算子，通过最小二乘拟合得到的重建算子具有最小的算子范数，因此在有噪声测量时最稳定。接着构造了具有最小可能准最优常数的算子，该算子在采样前出现的系统误差（模型不确定性）下最稳定。通过连续变化两种重建方法，可以实现稳定性和准最优性的权衡。作为应用，研究了从非均匀采样其傅里叶变换来重建具有紧支撑的函数。
Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient conditions, which are straightforward to verify, are obtained that ensure that a given matrix weight is contained in the Muckenhoupt matrix $A_p$ class. Applications to singular integral operators with product kernels are considered.
In this paper we study $A$-projections, i.e. operators of a Hilbert space $\HH$ which act as projections when a seminorm is considered in $\HH$. $A$-projections were introduced by Mitra and Rao \cite{[MitRao74]} for finite dimensional spaces. We relate this concept to the theory of compatibility between positive operators and closed subspaces of $\HH$. We also study the relationship between weighted least squares problems and compatibility.
We obtain ceratin estimates for the reproducing kernels of large weighted Bergman spaces. Applications of these estimates to boundedness of the Bergman projection on $L^p(\D,ω^{p/2})$, complex interpolation and duality of weighted Bergman spaces are given.
For the weight function $\prod_{i=1}^{d+1}|x_i|^{2\k_i}$ on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the convergence of the Cesàro $(C,δ)$ means in the weighted $L^p$ space for $δ$ below the critical index. Similar results are also proved for corresponding weight functions on the unit ball and on the simplex.
Weighted projections and Riesz frames
本文通过定义子空间与对角算子代数的相容性，研究加权投影并给出Riesz框架的新刻画。
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to the closure of their ranges is described.
Random Frame Decompositions from Weighted Residual Flows
本文提出了一种基于加权残差流的随机框架生成方法，通过正交投影的迭代构造，实现了正算子的强收敛分解，并在特定条件下生成随机Parseval框架。
Weak-type bounds for the Bergman projection with Bekollé-Bonami weights
针对带Bekollé-Bonami权的Bergman投影，本文建立其加权弱型界，给出改进的弱型(1,1)估计的两种证明及p>1时的精确弱型(p,p)界等结果，相关结论在经典情形下也属全新。
Given a weight function, we define the Bergman type projection with values in the corresponding weighted Bergman space on the unit ball $\mathbb B_n$ of $\mathbb C^n, n>1$. We characterize the radial weights such that this projection is bounded from $L^\infty$ to the Bloch space $\mathcal B$.
In this note we study some basic properties of general fractional derivatives induced by weighted Bergman kernels. As an application we demonstrate a method for generating pre-images of analytic functions under weighted Bergman projections. This approach is useful for proving the surjectivity of weighted Bergman projections in cases when the target space is not a subspace of the domain space (such situations arise often when dealing with Bloch and Besov spaces). We also discuss a fractional Littlewood-Paley formula.
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces $\mathcal{E} = \{E_i \}_{i\in I}$ of a Hilbert space $\mathcal{K}$ and a surjective $T\in L(\mathcal{K}, \mathcal{H})$ in order that $\{T(E_i)\}_{i\in I}$ is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J. A. Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames. P…
Alternating Weighted Residual Flows and the Non-Commutative Gap
本文提出了一种非线性交替加权残差流方法，用于分析非交换算子的极限行为，并揭示其与经典短算子之间的关系。
Strong and weak-type estimates for radial weighted Bergman projections
研究单位圆盘上由径向权重诱导的伯格曼投影的\(L^p\)有界性，通过建立二分法及相关条件刻画，证实佩莱兹 - 拉蒂亚猜想，解决多斯塔尼奇在2004年提出的问题。
Weighted endpoint bounds for the Bergman and Cauchy-Szegő projections on domains with near minimal smoothness
研究近最小光滑性域上Bergman和Cauchy-Szegő投影的加权端点界，证明了弱型$(1,1)$性质并推导出加权Kolmogorov和Zygmund不等式。
We describe the range of of weighted Cauchy transform and its $k$-Bergman projection when action on weighted true poly-Bargmann spaces constituting an orthogonal Hilbertian decomposition of the Hilbert space of Gaussian functions on the complex plane.
Weighted Minkowski's Existence Theorem and Projection Bodies
本文建立连续密度 Borel 测度类上的加权 Minkowski 存在定理，并分类加权投影体、解决同构 Shephard 问题的关键情形。
In this paper we solve a problem posed by H. Bommier-Hato, M. Engliš and E.H. Youssfi in [3] on the boundedness of the Bergman-type projections in generalized Fock spaces. It will be a consequence of two facts: a full description of the embeddings between generalized Fock-Sobolev spaces and a complete characterization of the boundedness of the above Bergman type projections between weighted $L^p$-spaces related to generalized Fock-Sobolev spaces.
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