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Using a result of J-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf $F$ on a real manifold and an integer $k$, if two functions vanish on the truncated microsupport $Ss_k(F)$, then so does…
We prove a montonicity property of the new basis of C[(Z/2)^D]. We also study the matrix coefficients of the Fourier transform with respect to the new basis and formulate a conjecture for them.
We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these…
We prove a nonsmooth implicit function theorem applicable to the zero set of the difference of convex functions. This theorem is explicit and global: it gives a formula representing this zero set as a difference of convex functions which…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
We study the dynamics of $L^p$-multipliers on non-compact simply connected harmonic manifolds of purely exponential volume growth. These are linear operators on the $L^p$-spaces which behave nicely on radial functions under Fourier…
It is a classical theorem that if a function is integrable along the boundary of the unit circle, then the function is the nontangential limit of a holomorphic function on the open disc if and only if its Fourier coefficients for…
In this paper we establish decay estimates for Fourier transform on Hardy-Morrey spaces and its localizable version. Our work include some aspects to these spaces linked up with pointwise Fourier estimates, in particular a natural approach…
Exclusive nonleptonic bottom meson decays are studied in the covariant osillator quark model using the factorization assumption. The main feature of this model is that it can simultaniously be applied to both heavy to heavy and heavy to…
On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…
We consider the boundary dynamics of iterated function systems of holomorphic self-maps of the unit disc. Our main result provides a sufficient condition which guarantees that the dynamical behaviour of a left iterated function system in…
In this note, we investigate $C^2$ differential images of the homogeneous self-similar measure associated with an IFS $\mathcal{I}=\{\rho x+a_j\}_{j=1}^m$ satisfying the strong separation condition and a positive probability vector…
We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of…
We establish power Fourier decay for equilibrium states of parabolic $C^{1+\alpha}$ iterated function systems with overlaps satisfying a multiscale nonlinearity condition. This class includes the Lyons conductance measures $\nu_t$, $0<t<1$,…
We show positivity of the lower Fourier dimension for equilibrium states of nonlinear, area preserving, Axiom A diffeomorphisms on surfaces. To do so, we use the sum-product phenomenon to reduce Fourier decay to the study of some temporal…
Let $\Gamma$ be a (convex-)cocompact group of isometries of the hyperbolic space $\mathbb{H}^d$, let $M := \mathbb{H}^d/\Gamma$ be the associated hyperbolic manifold, and consider a real valued potential $F$ on its unit tangent bundle $T^1…
We demonstrate the presence of modular properties in partition functions of $T\bar{T}$ deformed conformal field theories. These properties are verified explicitly for the deformed free boson. The modular features facilitate a derivation of…
We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…
In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that if a function $f$ has decay $f=O(r^{-1-\varepsilon}) $ for…
We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…