A few words on the second edition. By a nice coincidence, Springer's proposal to revise the
book came when I was giving a serious thought to the idea. Ten years have passed and my …

In this paper we treat the two-variable positive extension problem for trigonometric
polynomials where the extension is required to be the reciprocal of the absolute value …

Antenna arrays with shaped power patterns have many applications in communications and
radars. Many antenna array synthesis techniques for shaped patterns have been developed …

This paper develops a new mathematical framework for denoising in blind two-dimensional
(2D) super-resolution upon using the atomic norm. The framework denoises a signal that …

We propose a characterization of multivariate trigonometric polynomials that are positive on
a given frequency domain. The positive polynomials are parameterized as a linear function …

We consider the problem to estimate the generalized cepstral coefficients of a stationary
stochastic process or stationary multidimensional random field. It turns out that a naive …

Recently Dritschel proved that any positive multivariate Laurent polynomial can be
factorized into a sum of square magnitudes of polynomials. We first give another proof of the …

Abstract The Fejér-Riesz theorem has inspired numerous generalizations in one and
several variables, and for matrix-and operator-valued functions. This paper is a survey of …

Abstract In a recent work [19], Muirhead has studied level-set percolation of (discrete or
continuous) Gaussian fields, and has shown sharpness of the associated phase transition …

A recent paper of A. Connes and WD van Suijlekom [Comm. Math. Phys. 383 (2021), pp.
2021–2067] identifies the operator system of $ n\times n $ Toeplitz matrices with the dual of …