E. Alizadeh, M. H. Faroughi, M. Rahmani
In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g frames. Then, we give necessary and sufficient conditions on c-K-frames to characterize them. Finally, we verify perturbation of c-K-g-frames.
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The paper is devoted to continuous frames and Riesz bases in Hilbert C*-modules. we define a continuous Riesz basis for Hilbert C*-modules and give some results about them.
Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames in Hilbert $C^{\ast}$-Modules under perturbation and we establish some properties
In this paper we introduced the concept of continuous relay fusion frames in Hilbert spaces. And we define the dual frames for continuous relay fusion frames. Finally we study the perturbation probleme of continuous relay fusion frames.
In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will be clarified through examples.
In the present paper the notion of continuous frames is introduced and some results of these frames are proved. Next, we give the concept of duals of continuous frames in Hilbert C*-modules and investigate some properties of them.
Continuous frames in n-Hilbert spaces and their tensor products
该研究提出n-希尔伯特空间中连续框架的概念，将其推广至n-希尔伯特空间的张量积场景，并进一步研究了对应空间及张量积下的对偶连续框架与连续Bessel乘子。
We introduce the notion of continuous controlled g-fusion frame in Hilbert space which is the generalization of discrete controlled g-fusion frame and give an example. Some characterizations of continuous controlled g-fusion frame have been presented. We define the frame operator and multiplier of continuous controlled g-fusion Bessel families in Hilbert spaces. Continuous resolution of the identity operator on a Hilbert space using the theory of continuous controlled g-fusion frame is being considered. Finally, we discuss perturbation results of continuous controlled g-fusion frame.
In this paper, we introduce and we study the concept of Continuous Controlled K-Frame for Hilbert $C^{\ast}$-Modules wich are generalizations of discrete Controlled K-Frames.
In this paper, we characterize and study the concept of controlled continuous $g$-frame which is an extension of continuous $g$-frame in Hilbert spaces. We introduce the concept of controlled continuous dual $g$-frame and observe some interesting properties of it. Finally, we characterize all controlled continuous dual $g$-frames of a controlled continuous $g$-frame.
Introduction to Continuous biframes in Hilbert spaces and their tensor products
本文引入Hilbert空间及其张量积中连续biframe的概念，验证了表示定理，借助可逆算子给出刻画，并研究了对偶连续biframe与连续biframe Bessel乘子。
Pairs of Woven continuous frames in Hilbert spaces
该研究引入希尔伯特空间的连续交织框架概念，提出构造交织连续框架对的新方法，推导其与对偶框架相关的新性质，并给出基于微小扰动的构造途径，丰富了连续框架理论。
Continuous biframes in Hilbert Spaces
该研究提出希尔伯特空间中连续双框架的概念，探究其以双框架算子为核心的基本性质，并引入新型连续双框架-Riesz基，丰富了希尔伯特空间的框架理论。
Frame Theory has a great revolution for recent years. This Theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. The purpose of this paper is the introduction and the study of the new concept that of Continuous Controlled K-g-Frame for Hilbert $C^{\ast}$-Modules wich is a generalizations of discrete Controlled K-g-Frames in Hilbert $C^{\ast}$-Modules. Also we establish some results.
The frame theory is dynamic and exciting with various pure and applied mathematics applications. In this paper, we introduce and study the concept of Controlled Continuous $\ast$-$g$-Frames in Hilbert $C^{\ast}$-Modules, which is a generalization of discrete controlled $\ast$-$g$-Frames in Hilbert $C^{\ast}$-Modules. Also, we give some properties.
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of frames in Hilbert spaces. In this papers we study the notion of dual continuous $K$-frames in Hilbert spaces. Also we etablish some new properties.
Continuous K-biframes in Hilbert spaces
本文提出希尔伯特空间中连续K-双框架的概念，通过构造多种例子并从算子理论角度建立其性质，拓展了框架理论的研究。
Exact Continuous frames in Hilbert C*-modules
该研究探讨 Hilbert C*-模中连续框架对偶的性质，并刻画删除框架元素后连续框架是否仍得以保持的条件。
In this paper, we introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames. Then, as an application we provide some fundamental identities and inequalities for semi-continuous $g$-frames. Finally, we present a classical perturbation result and prove that semi-continuous $g$-frames are stable under small perturbations.
Continuous generalized atomic subspaces for operators in Hilbert spaces
研究借助连续 g-融合框架理论定义有界线性算子的连续 g-原子子空间，得到恒等算子的连续分解，并提出连续 g-融合 Bessel 序列对的连续框架算子。
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $Ω$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.
Continuous K-biframes in Hilbert spaces and their tensor products
该研究推广了希尔伯特空间的连续双标架，提出连续K-双标架概念，给出其刻画、代数性质及借助有界线性算子的构造方法，建立其与商算子的关系，还定义了张量积空间上的连续K-双标架并给出示例。
On perturbation of continuous frames in Hilbert C*-modules
本文将 Hilbert 空间框架的 Casazza-Christensen 扰动定理推广至 Hilbert C*-模中的连续框架，得到了 Riesz 型框架扰动保持不变的必要条件，并探讨了算子框架接近性对连续 Bessel 映射成为连续框架的影响。
This paper presents a number of Kantorovich type integral inequalities involving tensor products of continuous fields of bounded linear operators on a Hilbert space. Kantorovich type inequality in which the product is replaced by an operator mean is also considered. Such inequalities include discrete inequalities as special cases. Moreover, some generalizations of an additive Gruss integral inequality for operators are obtained.
Frame theory is an exciting, dynamic and fast paced subject with applications in numerous fields of mathematics and engineering. In this paper we study Continuous Frame and introduce Continuous Frame with $C^{\ast}$-valued bounds. Also, we establich some properties.
Continuous biframes in Hilbert $C^{\ast}-$modules
该研究引入希尔伯特$C^{\ast}-$模的连续双框架概念，借助可逆可伴算子刻画其特征，研究相关Bessel乘子与对偶框架，并拓展至张量积场景给出相关性质。
In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include Anti-Wick operators, STFT multipliers or Calderón- Toeplitz operators. Due to the possible peculiarities of the underlying measure spaces, continuous frames do not behave quite as well as their discrete counterparts. Nonetheless, many results similar to the discrete case are proven for continuous frame multipliers as well, for instance compactness and Schatten class properties. F…
Continuous bi-g-frames for operators in Hilbert spaces
该研究在希尔伯特空间框架下提出连续双g-框架与连续K-双g-框架新概念，借助双框架算子分析其性质，并推导两类序列的稳定性结论，丰富了框架理论相关研究。
Continuous $K$-$g$-frames in Hilbert $C^*$-modules
本文将g-框架与K-框架概念结合，在Hilbert C*-模中引入并研究连续K-g-框架，证明其若干刻画，并建立连续K-g-对偶的存在性结果。
In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors from these frames, we will present a necessarily and sufficient condition about c-woven and c-fusion woven. Finally, perturbation of these frames will be introduced.
Construction of continuous controlled K-g-fusion frames in Hilbert spaces
本文提出了Hilbert空间中连续受控K-g-融合框架的概念，作为离散框架的推广，研究了其刻画、与商算子的关系及稳定性。
Weaving continuous controlled K-g-fusion frames in Hilbert spaces
该研究在希尔伯特空间中提出编织连续受控K-g-融合框架概念，给出其若干刻画，推广了两类已有框架的相关结果，并研究了该框架的扰动性质。
In this paper, we investigate some characterizations of dual continuous frames and give some results about them. Also, we refer to the method of constructing a family of duals through a fixed dual and show there exists a one-to-one correspondence between duals of a continuous frame for Hilbert $C^*$-module $U$ and adjointable operators $K$ from $U$ to $L^{2}(Ω,\mathcal A)$. Then we check the conditions that the sum of two duals of a given continuous frame under the influence of adjointable mappings becomes a dual of it and state some results about them.
Construction of continuous K-g-Frames in Hilbert $C^{\ast}$-Modules
本文在Hilbert $C^{\ast}$-模中研究连续K-g-框架的构造与和，给出可共轭算子的充要条件以生成新框架，并讨论其和的特征。
Continuous generalized fusion frame theory was recently introduced by Rahimi and al. Several equalities and inequalities have been obtained for frame, fusion generalized fusion frame, among others. In the present paper, we continue and extend these results to obtain some important identities and inequalities in the case of continuous generalized fusion frame, Parceval continuous generalized fusion frame, $ λ$-tight continuous generalized fusion frame. Moreover, we obtain some new inequalities for the alternate dual continuous generalized fusion frame. Finally, we obtain frame operator of a pai…
Suppose that S is a left amenable semitopological semigroup. We prove that if ${T_{t}: t \in S}$ is a uniformly k-Lipschitzian semigroup on a bounded closed and convex subset C of a Hilbert space and $k<\sqrt{2}$, then the set of fixed points of this semigroup is a Hölder continuous retract of C. This gives a qualitative complement to the Ishihara-Takahashi fixed point existence theorem.
Trace-Controlled Operator Selection and Discretization of Continuous Frames in Hilbert \(C^*\)-Modules
本文针对有限维$C^*$-代数上的Hilbert $C^*$-模，提出迹控制算子选择定理，并应用于连续框架的离散化，得到具有显式框架界和受控分离的采样族。
In this paper, we introduce the concept of Continuous $\ast$-g-Frame in Hilbert $C^{\ast}$-Modules and we establish some results. We also discuss the stability problem for Continuous $\ast$-g-Frame.
Frame Theory has a great revolution in recent years, this Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. The purpose of this paper is the introduction and the study of the concept of Controlled Continuous g-Frames in Hilbert $C^{\ast}$-Modules. Also we give some properties.
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Results on Continuous $K$-frames for Quaternionic (Super) Hilbert Spaces
本文探讨了四元数 Hilbert 空间中的连续 $K$-框架，研究了单个空间及超空间的 $K_1 \oplus K_2$-框架，并分析了它们与各子空间框架间的关系与对偶性。
We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a Hilbert space may be sampled to obtain a frame.
In this paper, we introduce the concept of Continuous $\ast$-K-g-Frame in Hilbert $C^{\ast}$-Modules and we give some properties.
We show that if the Hilbert transform with values in a Banach space is $L^p$ bounded, then so is the dyadic Hilbert transform, with a linear relation of the norms.
Let $K$ be a compact Hausdorff space and let $H$ be a real or complex Hilbert space with dim$(H_\mathbb{R})\geq 2$. We prove that the space $C(K,H)$ of all $H$-valued continuous functions on $K$, equipped with the supremum norm, satisfies the Mazur--Ulam property, that is, if $Y$ is any real Banach space, every surjective isometry $Δ$ from the unit sphere of $C(K,H)$ onto the unit sphere of $Y$ admits a unique extension to a surjective real linear isometry from $C(K,H)$ onto $Y$. Our strategy relies on the structure of $C(K)$-module of $C(K,H)$ and several results in JB$^*$-triple theory. For …
In this note, following the theory of discrete frame perturbations in a complex Hilbert space, we examine perturbation of rank $n$ continuous frame, rank $n$ continuous Bessel family and rank $n$ continuous Riesz family in a non-commutative setting, namely in a right quaternionic Hilbert space.
Given an uncountable, compact metric space, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on this compact space.
Almost sure linear independence of absolutely continuous Hilbert space-valued random vectors with respect to a special class of Hilbert space probability measures
本文研究无限维 Hilbert 空间中随机向量的线性无关性，证明在有限维子空间相对概率测度可忽略时，绝对连续分布可保证无需约束张成空间的随机维数。
We show that if the dyadic Hilbert transform with values in a Banach space is $L^p$ bounded, then so is the Hilbert transform, with a linear relation of the bounds. This result is the counterpart of [arXiv:2212.00090] where the opposite bound was proven.
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may not be defined. To overcome this problem, the new concept namely Q-dual for c-fusion frames will be defined and some of its properties will be investigated.
Strongly continuous fields of operators over varying Hilbert spaces
本文提出局部凸空间连续场概念，建立变 Hilbert 空间上无界自伴算子强连续族理论，可处理非局部平凡丛上的算子族，无需识别算子。
The Kaczmarz Algorithm in Hilbert $C^{*}$-modules
本文将Kaczmarz算法推广到Hilbert $C^*$-模，证明其可一致恢复Hilbert空间中的连续元素族，并通过归一化Cauchy变换给出标准框架可由该算法生成并实现为有界算子轨道的充分条件。
In this work, generalization of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.
k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by continuous super positions. We construct a continuous k-frame, so called ck-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a ck-frame and we prove some new results about it.
In this paper, we study the representation of orthogonally additive mappings acting on Hilbert $C^*$-modules and Hilbert $H^*$-modules. One of our main results shows that every continuous orthogonally additive mapping $f$ from a Hilbert module $W$ over $\K(\H)$ or $\H§(\H)$ to a complex normed space is of the form $f(x)=T(x)+Φ(< x, x >)$ for all $x\in W$, where $T$ is a continuous additive mapping, and $Φ$ is a continuous linear mapping.
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding approximate solutions to boundary value problems; using multiresolution-subdivision schemes in continuous domains. In this paper, we turn the tables: our object of study is realistic infinite discrete models in their own right; and we then use an analysis of suitable continuous counterpart problems, but now serving as a tool for obtaining solutions in the discrete wor…
Few years ago Găvruţa gave the notions of $K$-frame and atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$ in order to decompose $\mathcal{R}(K)$, the range of $K$, with a frame-like expansion. These notions are here generalized to the case of a densely defined and possibly unbounded operator on a Hilbert space $A$ in a continuous setting, thus extending what have been done in a previous paper in a discrete framework.
Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces
本文研究了在连续嵌入的Hilbert空间中随机偏微分方程子流形的随机不变性条件，并建立了其与有限维SDEs不变性之间的联系，提出了一种新的分析方法。
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