泛函分析

We study the cone of non-negative polynomials on generalized elliptic curves. We show that the zero set of every extreme ray has dense real points. If a generalized elliptic curve is embedded via a complete linear system, then we show that…

In the present paper, we study the norms for symmetric and antisymmetric tensor products of weighted shift operators. By proving that for $n\geq 2$, $$\|S_{\alpha}^{l_1}\odot\cdots \odot S_{\alpha}^{l_k}\odot…

We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and…

We construct a reflexive Banach space $X_\mathcal{D}$ with an unconditional basis such that all spreading models admitted by normalized block sequences in $X_\mathcal{D}$ are uniformly equivalent to the unit vector basis of $\ell_1$, yet…

We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescoping energy residuals" in particular. We prove new results…

We explain how to formulate Voiculescu's non-commutative Riemann sphere framework for fully matricial functions \cite{v10} within the theory of nc functions developed by Vinnikov and Kaliuzhnyi-Verbovetskyi \cite{kvv14}. We then extend this…

The Wodzicki residue is the unique trace on the algebra of classical pseudodifferential operators on a closed manifold, and Connes in 1988 proved that it coincides with the Dixmier trace. A Carnot manifold is a manifold $M$ whose tangent…

Let $S(C_0(X))^+$ and $S(C_0(Y))^+$ denote the positive parts of the unit spheres of $C_0(X)$ and $C_0(Y)$, where $X$ and $Y$ are locally compact Hausdorff spaces. We prove that every surjective isometry from $S(C_0(X))^+$ onto…

We study a sampling problem for the abstract wavelet transform associated with the quasiregular representation of the $SE(2)$ group, for a modulated gaussian mother wavelet. This problem is motivated by the behavior of brain's primary…

We investigate the minimum modulus analogue of the weak maximizing property, termed the \emph{weak minimizing property}. We establish that the pairs $(\ell_p, L^p[0, 1])$ for $2 \leq p < \infty$ and $(\ell_s \oplus_q \ell_q, \ell_r \oplus_p…

We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these…

Given a commuting $n$-tuple of bounded linear operators on a Hilbert space, together with a distinguished cyclic vector, Jim Agler defined a linear functional $\Lambda_{\mathbf{T},h}$ on the polynomial ring…

We study rearrangement-invariant spaces $X$ over $[0,\infty)$ for which there exists a function $h:(0,\infty)\to (0,\infty)$ such that \[ \|D_rf\|_X = h(r)\|f\|_X \] for all $f\in X$ and all $r>0$, where $D_r$ is the dilation operator. It…

This paper investigates triangle functions induced by tensor products of triangular norms and conorms. For any left continuous t-norm $T$ on $[0,1]$ and any right continuous t-conorm $L$ on $[0,\infty]$, the tensor product $L\otimes T$…

The image of a given orthonormal basis for a separable Hilbert space $\mathcal{H}$ under a bijective, bounded, and linear operator acting on $\mathcal{H}$ is called a Riesz basis of $\mathcal{H}$. Contrary to what happens with Riesz bases…

We present a general and natural framework to study the dynamics of composition operators on spaces of measurable functions, in which we then reconsider the characterizations for hypercyclic and mixing composition operators obtained by…

We prove an extended Granger-Johansen representation theorem (GJRT) for finite or infinite order integrated autoregressive time series on Banach space. We assume only that the resolvent of the autoregressive polynomial for the series is…

We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. spaces). More specifically, we focus on studying the…

We study the function $\varphi_1$ of minimal $L^1$ norm among all functions $f$ of exponential type at most $\pi$ for which $f(0)=1$. This function, first studied by H\"{o}rmander and Bernhardsson in 1993, has only real zeros $\pm \tau_n$,…

In this paper, we study the norm-controlled inversion problem in two classes of algebras of integrable functions. In contrast of the classical case of $L^{1}(G)$, we prove that this problem has a positive solution in our setting without any…