相关论文: On Function Theory in Quantum Disc: Invariant Kern…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
We consider the problem of computation of the correlation functions for the z-measures with the deformation (Jack) parameters 2 or 1/2. Such measures on partitions are originated from the representation theory of the infinite symmetric…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
In the classical Hardy space $H^2(\mathbb{D})$, it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator $S^{*}$. It…
Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical…
Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…
Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g.…
Let g be a Banach Lie algebra and \tau : g ---> g an involution. Write g=h+q for the eigenspace decomposition of g with respect to \tau and g^c := h+iq for the dual Lie algebra. In this article we show the integrability of two types of…
We give an explicit integral formula for the Dunkl kernel associated to root system of type $A_2$ and parameter $k>0$, by exploiting recent result in [1].
In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…
In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS…
We use Berezin's quantization procedure to obtain a formal $U_q su_{1,1}$-invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators are produced.
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral representation of zonal valuations involving mixed area measures…
Quantum variational algorithms have been one of major applications of quantum computing with current quantum devices. There are recent attempts to establish the foundation for these algorithms. A possible approach is to characterize the…
For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds…