Characterizations of those Ideals in L1 (R) which can be Synthesized.
Characterizations of tight frame wavelets with special dilation matrices.
Characterizing Sidon sets by interpolation properties of subsets
Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups containing...
Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections
We characterize those anisotropic Sobolev spaces on tori in the and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].
Charakterisierungen von nirgends differenzierbaren Weierstraß-Funktionen durch Replikativität.
Checkerboards, Lipschitz functions and uniform rectifiability.
In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof.Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε.Here Hk denotes k-dimensional Hausdorff measure and B(0,1) the unit ball in Rn. By iterating our proof we obtain a slightly stronger result which allows us...
Chirps -dimensionnels et analyse -microlocale
Ciesielski and Franklin systems
A short survey of results on classical Franklin system, Ciesielski systems and general Franklin systems is given. The principal role of the investigations of Z. Ciesielski in the development of these three topics is presented. Recent results on general Franklin systems are discussed in more detail. Some open problems are posed.
Classical 2-orthogonal polynomials and differential equations.
Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials
In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.
Classical boundary value problems for integrable temperatures in a domain
Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with -base and data in , a subspace of 1. We derive our results, considering the action of an adjoint operator on , a predual of , and using known properties of this last space.
Clifford algebras and the higher dimensional Cauchy integral
Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.
In the Fourier theory of functions of one variable, it is common to extend a function and its Fourier transform holomorphically to domains in the complex plane C, and to use the power of complex function theory. This depends on first extending the exponential function eixξ of the real variables x and ξ to a function eizζ which depends holomorphically on both the complex variables z and ζ .Our thesis is this. The natural analog in higher dimensions is to extend a function of m real variables monogenically...
Clifford and harmonic analysis on cylinders and torii.
Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...
Clifford-Hermite Wavelets in Euclidean Space.
CLO spaces and central maximal operators
We consider central versions of the space studied by Coifman and Rochberg and later by Bennett, as well as some natural relations with a central version of a maximal operator.
Closure of dilates of shift-invariant subspaces
Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a...
Coarea integration in metric spaces
Let be a metric space with a doubling measure, be a boundedly compact metric space and be a Lebesgue precise mapping whose upper gradient belongs to the Lorentz space , . Let be a set of measure zero. Then for -a.e. , where is the -dimensional Hausdorff measure and is the -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...
Coefficient multipliers on spaces of vector-valued entire Dirichlet series
The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...
Comment on and a characterization of the concept of complete residuated lattice.