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Extending the classical notion of the spreading model, the $k$-spreading models of a Banach space are introduced, for every $k\in\mathbb{N}$. The definition, which is based on the $k$-sequences and plegma families, reveals a new class of…
This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an…
Classically, Tannaka-Krein duality allows us to reconstruct a (co)algebra from its category of representation. In this paper we present an approach that allows us to generalise this theory to the setting of Banach spaces. This leads to…
Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's…
The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…
We introduce the notion of Krein-operator convexity in the setting of Krein spaces. We present an indefinite version of the Jensen operator inequality on Krein spaces by showing that if $(\mathscr{H},J)$ is a Krein space, $\mathcal{U}$ is…
In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics…
The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least $C^2$-smooth…
The main result of this paper is a description of the space of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. This space coincides with the space of…
We prove a number of results on integrability and extendability of Lie algebras of unbounded skew-symmetric operators with common dense domain in Hilbert space. By integrability for a Lie algebra $\mathfrak{g}$, we mean that there is an…
In this research article, we formulate and prove multidimensional Widder--Arendt theorem and integrated form of multidimensional Widder--Arendt theorem for functions with values in sequentially complete locally convex spaces. Established…
We develop a fundamental theory of compact quantum group equivariant finite extensions of C*-algebras. In particular we focus on the case of quantum homogeneous spaces and give a Tannaka-Krein type result for equivariant correspondences. As…
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated…
The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the…
The Hilbert space of level $q$ Chern-Simons theory of gauge group $G$ of the ADE type quantized on $T^2$ can be represented by points that lie on the weight lattice of the Lie algebra $\mathfrak{g}$ up to some discrete identifications. Of…
We realize the relative discrete series of a weighted $L^2$-space on a bounded symmetric doamin as kernels of invariant Cauchy-Riemann operator, and thus as the spaces of nearly holomorphic functions.
We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of…
We prove Strichartz estimates for a class of Baouendi--Grushin operators acting either on the Euclidean space or a product of the type $\mathbb{R}^{d_1} \times M$, where $(M,g)$ is a smooth compact manifold with no boundary. We then give an…