相关论文: On the (dis)continuity of the Fourier transform of…
Let K be a self-similar or self-affine set in R^d, let \mu be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation…
We study equivalent descriptions of the vague, weak, setwise and total-variation (TV) convergence of sequences of Borel measures on metrizable and non-metrizable topological spaces in this work. On metrizable spaces, we give some equivalent…
The main result of this paper is, that if we suppose that a function is absolutely continuous and uniformly H\"older continuous and that its finite difference function does not oscillate infinitely often on a bounded interval, then the…
We complete the theoretical framework required for the construction of a Morse homology theory for certain types of forced mean curvature flows. The main result of this paper describes the asymptotic behaviour of these flows as the forcing…
We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…
The support of wavelet transform associated with square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Pointwise homogeneous approximation property for wavelet transform has been…
A metric is formal if all products of harmonic forms are again harmonic. The existence of a formal metric implies Sullivan formality of the manifold, and hence formal metrics can exist only in presence of a very restricted topology. We show…
It is a well known general principle that the Fourier transform of a random measure is small, except at the zero frequency, in various senses for appropriate notions of randomness. In this note we develop analogues of this principle for two…
We investigate if a sharp topological transition in a metal with a large Fermi surface may be detected in transport measurements. In particular, we address if a skew scattering and a side jump on elastic disorder in the bulk of such a metal…
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by…
Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an…
Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
The Fourier series of continuous functions of constant absolute value have interesting properties : according to the main theorems of the article, if the coefficients with positive indexes are square-summable with respect to a certain…
We study Borel systems and continuous systems of measures, with a focus on mapping properties: compositions, liftings, fibred products and disintegration. Parts of the theory we develop can be derived from known work in the literature, and…
An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrodinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two…
We present a characterization of the sets that appear as Fourier spectra of measures in terms of the existence of a strongly continuous representation of the ambient group that has a wandering vector for the given set.
In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation…