Related papers: Restriction theorems for Hankel operators
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…
We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form…
The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Kernel methods are theoretically well-understood and as a result enjoy algorithmic…
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces where all the evaluation functionals are linear and bounded. They are in one-to-one correspondence with positive definite maps called kernels. Stable RKHSs enjoy the…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
We study the Grushin operators acting on $\mathbb{R}^{d_1}_x \times \mathbb{R}^{d_2}_t$ and defined by the formula \begin{equation*}…
The characterization of the boundedness of operators induced by Hankel matrices on analytic function spaces can be traced back to the work of Z. Nehari and H. Widom on the Hardy space, and has been extensively studied on many other analytic…
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
Let $A_{1},...A_{m}$ be a $n\times n$ invertible matrices. Let $0 \leq \alpha<n$ and $0<\alpha_{i}<n$ such that $\alpha_1 + ... + \alpha_m = n- \alpha$. We define% \begin{equation*} T_{\alpha}f(x)=\int \frac{1}{\left\vert…
We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
We derive the limiting matrix kernels for the the Gaussian Orthogonal and Symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that assure convergence of the determinants.
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…
This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…
The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on…
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…