Related papers: Hilbert spaces built on a similarity and on dynami…

Frames for Hilbert spaces are interesting for mathematicians but also important for applications e.g. in signal analysis and in physics. Both in mathematics and physics it is natural to consider a full scale of spaces, and not only a single…

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…

Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert…

Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span $L_X^2$ of $X$. This paper investigates…

We introduce a new route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and "lifting" to higher dimensions using subsystem symmetries…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

We investigate complex structures on twisted Hilbert spaces, with special attention paid to the Kalton-Peck $Z_2$ space and to the hyperplane problem. We consider (nontrivial) twisted Hilbert spaces generated by centralizers obtained from…

In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…

Our main goal is to track down an algebraic basis of Hilbert space $\ell^2$ which is a connected and locally connected subset of the unit sphere.

We construct a rigged Hilbert space for the square integrable functions on the line L^2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together,…

It is shown that the Hilbert geometry $(D,h_D)$ associated to a bounded convex domain $D\subset \mathbb{E}^n$ is isometric to a normed vector space $(V,||\cdot ||)$ if and only if $D$ is an open $n$-simplex. One further result on the…

We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…

The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2,2)-supersymmetric systems in 2-dimensional spacetime which are closely…

Zonotopal algebra interweaves algebraic, geometric and combinatorial properties of a given linear map X. Of basic significance in this theory is the fact that the algebraic structures are derived from the geometry (via a non-linear…

We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which…

Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…

For vector/AdS and dS holography we establish the structure of the emergent Hilbert space. This is done through implementation of finite $N$ trace relations on the infinite collective space. For fermionic theories a finite Hilbert space is…