16 citations · 37 across the 18 of their papers we have counts for
20 papers
Adaptive Quarklet Tree Approximation
Stephan Dahlke, Marc Hovemann, Thorsten Raasch +1
This paper is concerned with near-optimal approximation of a given function with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. I…
Anisotropic Besov regularity of parabolic PDEs
Stephan Dahlke, Cornelia Schneider
This paper is concerned with the regularity of solutions to parabolic evolution equations. Special attention is paid to the smoothness in the specific anisotropic scale $\ B^{r\mat…
Quarklet Characterizations for Triebel-Lizorkin Spaces
Marc Hovemann, Stephan Dahlke
In this paper we prove that under some conditions on the parameters the one-dimensional Triebel-Lizorkin spaces can be described in terms of quarklets.…
Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type
Stephan Dahlke, Cornelia Schneider
This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we…
Besov regularity of non-linear parabolic PDEs on non-convex polyhedral domains
Stephan Dahlke, Markus Hansen, Cornelia Schneider
This paper is concerned with the regularity of solutions to parabolic evolution equations. We consider semilinear problems on non-convex domains. Special attention is paid to the s…
Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited
S. Dahlke, F. De Mari, E. De Vito +5
In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible…
Properties of Kondratiev spaces
Stephan Dahlke, Markus Hansen, Cornelia Schneider +1
In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compa…
Besov regularity of parabolic and hyperbolic PDEs
Stephan Dahlke, Cornelia Schneider
This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in the specific sc…
On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel
Stephan Dahlke, Filippo De Mari, Ernesto De Vito +4
This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of…
Adaptive wavelet BEM for boundary integral equations: Theory and numerical experiments
Stephan Dahlke, Helmut Harbrecht, Manuela Utzinger +1
In this paper, we are concerned with the numerical treatment of boundary integral equations by means of the adaptive wavelet boundary element method (BEM). In particular, we consid…
Besov Regularity for the Stationary Navier-Stokes Equation on Bounded Lipschitz Domains
Frank Eckhardt, Petru A. Cioica-Licht, Stephan Dahlke
We use the scale , , , to study the regularity of the stationary Stokes equation on bounded Lipschitz domains , , wi…
Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings
Giovanni S. Alberti, Stephan Dahlke, Filippo De Mari +2
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had…
Continuous and discrete frames generated by the evolution flow of the Schrödinger equation
Giovanni S. Alberti, Stephan Dahlke, Filippo De Mari +2
We study a family of coherent states, called Schrödingerlets, both in the continuous and discrete setting. They are defined in terms of the Schrödinger equation of a free quantum p…
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs
Petru A. Cioica, Stephan Dahlke, Nicolas Döhring +6
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme…
Different faces of the shearlet group
Stefan Dahlke, Filippo De Mari, Ernesto De Vito +3
Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrabl…
Coorbit spaces with voice in a Fréchet space
Stephan Dahlke, Filippo De Mari, Ernesto De Vito +4
We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group that are not necessarily irreducible nor integrable. Ou…
Besov regularity for operator equations on patchwise smooth manifolds
Stephan Dahlke, Markus Weimar
We study regularity properties of solutions to operator equations on patchwise smooth manifolds such as, e.g., boundaries of polyhedral domains .…
Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains
Petru A. Cioica, Stephan Dahlke, Stefan Kinzel +4
We use the scale of Besov spaces B^α_{τ,τ}(O), α>0, 1/τ=α/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equat…
Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames
Stephan Dahlke, Erich Novak, Winfried Sickel
We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors a…
Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings II
Stephan Dahlke, Erich Novak, Winfried Sickel
We study the optimal approximation of the solution of an operator equation Au=f by linear and nonlinear mappings. We identify those cases where optimal nonlinear approximation is b…