Related papers: Oppenheim-Schur's inequality and RKHS

This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…

We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

In this paper the Jessen's type inequality for normalized positive $C_0$-semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint-semigroup, which does not give the analogous results…

Byusing equivalence conditions for sectorial matrices obtained by Alakhrass and Sababheh in 2020, we improve a Rotfel'd type inequality for sectorial matrices derived by P. Zhang in 2015 and generalize a result derived by Y. Mao et al. in…

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement…

Let $A$ be a positive semidefinite $m\times m$ block matrix with each block $n$-square, then the following determinantal inequality for partial traces holds \[ (\mathrm{tr} A)^{mn} - \det(\mathrm{tr}_2 A)^n \ge \bigl| \det A -…

We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral…

In this paper, we investigate the reverse improvement property of Sobolev inequalities on manifolds with quadratically decaying Ricci curvature. Specifically, we establish conditions under which the uniform decay of the heat kernel implies…

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…

A version of the Cauchy-Schwarz inequality in operator theory is the following: for any two symmetric, positive definite matrices $A,B \in \mathbb{R}^{n \times n}$ and arbitrary $X \in \mathbb{R}^{n \times n}$ $$ \|AXB\| \leq \|A^2…

A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…

For a family of the orthogonal $O(k)$ type Quantum Matrix algebras we establish an analogue of the Cayley--Hamilton theorem. The form of the Cayley-Hamilton identity is different in three cases. First, the cases of odd ($k=2\ell -1$) and…

Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…

We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that…

This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same…

Reproducing kernel Hilbert spaces (RKHSs) are very important function spaces, playing an important role in machine learning, statistics, numerical analysis and pure mathematics. Since Lipschitz and H\"older continuity are important…

In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.

We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…