相关论文: Landen survey
In this preprint the notion of deformation quantization of endomorphism bundles over symplectic manifolds is defined and developed, including index theory.
We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions…
The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $\mathbb{R}^n$. The degree of compactness will be measured in terms of related entropy numbers. We are more…
Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting…
The windowed ray transform is a natural generalization of the "Analytic-Signal Transform" which is developed to extend arbitrary functions from $\RR^n$ to $\CC^n$. We present several inversion formulas here.
In this paper our aim is to present some Landen inequalities for Gaussian hypergeometric functions, confluent hypergeometric functions, generalized Bessel functions and for general power series. Our main results complement and generalize…
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
A mathematical development of the Walsh transform, Walsh basis, and Walsh coefficients is given. The author was prompted to write this by a wish to give a unified treatment of epistatic coordinates as they are used in evolutionary biology.…
We study the local structure of vector fields on $\mathbb{R}^3$ which preserve the Martinet $1$-form $\alpha=(1+x)dy\pm zdz$. We present the classification of their singularities, up to diffeomorphisms preserving the form $\alpha$, as well…
The objective of this manuscript is to understand the structure of an invertible linear map on the space of real symmetric matrices $\mathcal{S}^n$ that leaves invariant the closed convex cones of copositive and completely positive matrices…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
We introduce a transformation of linear Pfaffian systems, which we call the middle Laplace transform, as a formulation of the Laplace transform from the perspective of Katz theory. While the definition of the middle Laplace transform is…
In this study, we give the dual characterizations of Mannheim offsets of the ruled surface in terms of their integral invariants and the new characterization of the Mannheim offsets of developable surface. Furthermore, we obtain the…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
An element of the algebra $M_n(\mathbb{F})$ of $n \times n$ matrices over a field $\mathbb{F}$ is called an involution if its square equals the identity matrix. Gustafson, Halmos, and Radjavi proved that any product of involutions in…
The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.