Related papers: Decay bounds for functions of matrices with banded…
In this paper we shall study noncommutative central moment inequalities with a main focus on whether the commutative bounds are tight in the noncommutative case, or not. We prove that the answer is affirmative for the fourth central moment…
We apply a recent theoretical analysis of hadronic observables in inclusive semileptonic heavy hadron decays to the phenomenology of $B$ and $D$ mesons. Correlated bounds on the nonperturbative parameters $\bar\Lambda$ and $\lambda_1$ are…
Martin boundaries and integral representations of positive functions which are harmonic in a bounded domain $D$ with respect to Brownian motion are well understood. Unlike the Brownian case, there are two different kinds of harmonicity with…
We investigate matrix-weighted bounds for the sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl. We extend their result to sublinear operators acting upon vector-valued functions. First, we dominate these…
We give a lower bound for the Waring rank and cactus rank of forms that are invariant under an action of a connected algebraic group. We use this to improve the Ranestad--Schreyer--Shafiei lower bounds for the Waring ranks and cactus ranks…
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…
We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its…
It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in…
This paper studies coarse compactifications and their boundary. We introduce two alternative descriptions to Roe's original definition of coarse compactification. One approach uses bounded functions on $X$ that can be extended to the…
Let $\det_2(A)$ be the block-wise determinant (partial determinant). We consider the condition for completing the determinant $\det(\det_2(A)) = \det(A),$ and characterize the case for an arbitrary Kronecker product $A$ of matrices over an…
In this paper, we give strong lower bounds on the size of the sets of products of matrices in some certain groups. More precisely, we prove an analogue of a result due to Chapman and Iosevich for matrices in $SL_2(\mathbb{F}_p)$ with…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing a banded matrix from a matrix-valued…
We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic…
Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical definitions--via power series, spectral calculus, or Jordan…
We determine the border subrank of higher order structure tensors of several families of algebras, and in particular obtain the following results. (1) We determine tight bounds on the border subrank of $k$-fold matrix multiplication and…
We consider "spectral" matrix-functions for Hermitian matrices, where the novelty is that the function applied to the spectrum is allowed to be a vector-field rather than a scalar function (a.k.a isotropic matrix functions). We prove first…
We discuss some simple H\"uckel-like matrix representations of non-Hermitian operators with antiunitary symmetries that include generalized $\mathcal{PT}$ (parity transformation followed by time-reversal) symmetry. One of them exhibits…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
Hadronic decays rates of the $\tau$ lepton into multi meson final states are presented. The structure of the hadronic matrix elements for various decay modes is discussed. The formalism of structure functions allows for a detailed test of…