相关论文: Towards a general distortion theory for univalent …

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…

Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…

The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…

We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…

We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on…

In this thesis we investigate a new formalism for supergeometry which focuses on the categorical properties of the theory. This approach is our main tool in the subsequent investigation of a global analytic approach to the construction of…

This paper is on $\Gamma$-convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. Here both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the…

In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Further, these results are extended to a…

In the study of holomorphic functions of one complex variable, one well-known theory is that of elliptic functions and it is possible to take the zeta-function of Weierstrass as a building stone of this vast theory. We are working the…

Assuming complex functions defined on complex curves satisfy recursion relations with respect to number of parameters, we express the corresponding cohomology theory via generalizations of holomorphic connections. In examples provided, the…

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…

We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…

The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…

To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known Cartan embedding for those spaces. This also leads to the…