Related papers: Transformation de Fourier homogene
Mellin transform of fibre integral is calculated for certain classes of non-degenerate affine complete intersections. The lattice structure of the poles of the Mellin transform is clarified by means of the mixed Hodge structure of the…
One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in $\mathbb{R}^n$. When the support is a smooth enough manifold, an almost…
Let $k $ be the algebraic closure of a finite field of odd characteristic $p$ and $X$ a smooth projective scheme over the Witt ring $W(k)$ which is geometrically connected in characteristic zero. We introduce the notion of Higgs-de Rham…
Let V be a finite dimensional vector space over the field with two elements with a given nondegenerate symplectic form. Let [V] be the vector space of complex valued functions on V and let [V]_Z be the subgroup of [V] consisting of integer…
Let ${\boldsymbol{G}}$ be a connected reductive group defined over a non--Archimedean local field $F$. Put $G={\boldsymbol{G}}(F)$. Let $\theta$ be an $F$--automorphism of ${\boldsymbol{G}}$, and let $\omega$ be a smooth character of $G$.…
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…
To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the…
We construct functors sending torus-equivariant quasi-coherent sheaves on toric schemes over the sphere spectrum to constructible sheaves of spectra on real vector spaces. This provides a spectral lift of the toric homolgoical mirror…
The purpose of this paper is to investigate the distribution of zeros of entire functions which can be represented as the Fourier transforms of certain admissible kernels. The principal results bring to light the intimate connection between…
We prove a filtered version of the Homotopy Transfer Theorem which gives an A-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the…
The Fourier-Mukai transform is lifted to the derived category of sheaves with connection on abelian varieties. The case of flat connections (D-modules) is discussed in detail.
We generalise Kahn, Miyazaki, Saito, Yamazaki's theory of modulus pairs to pairs $(X, D)$ consisting of a qcqs scheme $X$ equipped with an effective Cartier divisor $D$ representing a ramification bound. We develop theories of sheaves on…
In this short notes, we prove a stronger version of Theorem 0.6 in our previous paper arXiv:1709.01485: Given a smooth log scheme $(\mathcal{X} \supset \mathcal{D})_{W(\mathbb{F}_q)}$, each stable twisted $f$-periodic logarithmic Higgs…
Fields of Lorentz transformations on a space--time are related to tangent bundle self isometries. In other words, a gauge transformation with respect to the Minkowski metric on each fibre. Any such isometry can be expressed, at least…
We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for…
The Radon transform Rf of functions f on SO(3) has recently been applied extensively in texture analysis, i.e. the analysis of preferred crystallographic orientation. In practice one has to determine the orientation probability density…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential…
It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr…
We explicitly identify the algebra generated by symplectic Fourier-Deligne transforms (i.e. convolution with Kazhdan-Laumon sheaves) acting on the Grothendieck group of perverse sheaves on the basic affine space $G/U$, answering a question…