The paper deals with $$L_p$$ -boundedness of the Hartley-Fourier convolutions operator and their applied aspects. We establish various new Young-type inequalities obtain structure a normed ring in Banach space when equipping it such convolutional multiplication. Weighted -norm these are also considered. As applications, we investigate solvability bounded $$L_1$$ -solution class Fredholm-type in...

The reliability of quantum channels for transmitting information is profound importance from the perspective information. This naturally leads to question as how well a state preserved when subjected channel. We propose measure quantumness based on non-commutativity states that intuitive and easy compute. apply proposed some known noise channels, both Markovian non-Markovian find results are in...

An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and$|T(x_1, x_n)|=\|T\|,$ where ${\mathcal denotes the space all continuous $n$-linear forms on $E.$For E),$ we define $${Norm}(T)=\Big\{(x_1, E^n: (x_1, x_n)~\mbox{is point of}~T\Big\}.$$${Norm}(T)$ set} $T$. We classify ${Norm}(T)$ for every L}_s(^3 l_{1}^2)$.

The channel estimation is one of important techniques to ensure reliable broadband signal transmission. Broadband channels are often modeled as a sparse channel. Comparing with traditional dense-assumption based linear channel estimation methods, e.g., least mean square/fourth (LMS/F) algorithm, exploiting sparse structure information can get extra performance gain. By introducing -norm penalty...

We consider the second-order asymptotic properties of‎  ‎the bootstrap of L_1 regression estimators by looking at‎ ‎the difference between the L_1 estimator and ‎its first-order approximation‎, ‎where the latter‎ ‎is the minimizer of a quadratic approximation to the‎ ‎L_1 objective function‎. ‎It is shown that the bootstrap ‎distribution of the normed difference does not converge‎ ‎(eit...

Let $\mathcal{X}$ be a Banach space with fundamental biorthogonal system and let $\mathcal{Y}$ the dense subspace spanned by vectors of system. We prove that admits $C^\infty$-smooth norm locally depends on finitely many coordinates (LFC, for short), as well polyhedral coordinates. As consequence, we also finite, $\sigma$-uniformly discrete LFC partitions unity $C^1$-smooth LUR norm. This theor...

We consider the use of sparsity-promoting norms in obtaining localised forcing structures from resolvent analysis. By formulating optimal problem as a Riemannian optimisation, we are able to maximise cost functionals whilst maintaining unit-energy forcing. Taking functional be energy norm driven response results traditional analysis and is solvable by singular value decomposition (SVD). modifyi...

Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this paper, we propose a novel framework that uses error function to approximate unit step function. It can be considered surrogate for $L_0$ norm. The asymptotic...