Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

More documents

Recommendations

Info

$Dr. Kai Zehmisch SS 2013 Dipl.-Math. Hella Timmermann 3 ...$

$Prof. Dr. W. Wefelmeyer WS 2004/05 Dipl.-Math. K. Tang Übungen ...$

DMV Tagung 2011 - Köln, 19. - 22. September Bastian Harrach Technische Universität München Fast shape-reconstruction in electrical impedance tomography The mathematical problem behind electrical impedance tomography (EIT) is how to reconstruct the coefficient σ(x) in the elliptic partial differential equation from knowledge of the Neumann-to-Dirichlet operator ∇ · σ(x)∇u(x) = 0, x ∈ Ω, (3) Λ(σ) : g ↦→ u| ∂Ω, u solves (3). We concentrate on the following anomaly detection (or shape detection) problem in EIT. Assume that σ differs from a known reference conductivity σ0 only in a (possibly disconnected) open subset D with D ⊂ Ω, σ(x) = σ0 + σD(x)χD(x), where χD(x) denotes the characteristic function of D. Our goal is to locate the conductivity anomalies D from Λ(σ). Somewhat surprisingly, linearizing the inverse problem of EIT does not lead to shape errors (Harrach/Seo, 2010). Based on this result, we will derive fast shape reconstruction methods in this talk. Literatur Harrach, B., Seo, J. K. (2010). Exact shape-reconstruction by one-step linearization in electrical impedance tomography. SIAM J. Math. Anal., 42, 1505 - 1518. 114
DMV Tagung 2011 - Köln, 19. - 22. September Sören Häuser Technische Universität, Kaiserslautern Shearlet coorbit spaces: traces and embeddings In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the shearlet transform has the outstanding property to stem from a square integrable group representation. This remarkable fact provides the opportunity to design associated canonical smoothness spaces, so-called shearlet coorbit spaces by applying the general coorbit theory derived by Feichtinger and Gröchenig. However, once these abstract smoothness space are established some natural questions arise. Of course one would like to know how these spaces look like and how they are related to other known classical smoothness spaces such as Besov or Triebel-Lizorkin spaces. Moreover, one would like to understand the structure of these new spaces. That is, it would be desirable to know how these new scales of shearlet coorbit spaces behave under embeddings and trace operations. In this talk we examine structural properties of shearlet coorbit spaces in higher dimensions. We prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone in three dimensions into Besov spaces. The results are based on general atomic decompositions of Besov spaces. Furthermore, we establish trace results for these subspaces with respect to the coordinate planes. It turns out that in many cases these traces are contained in lower dimensional shearlet coorbit spaces. To prove these results we apply the concept of coorbit molecules recently developed by Gröchenig and Piotrowski. Joint work with S. Dahlke (Philipps-Universität Marburg), G. Steidl (Technische Universität Kaiserslautern) and G. Teschke (Hochschule Neubrandenburg). Lutz Kämmerer Technische Universität Chemnitz Stable interpolation of hyperbolic cross trigonometric polynomials A straightforward discretisation of high-dimensional problems often leads to an exponential growth in the number of degrees of freedom. So, computational costs of even efficient algorithms like the fast Fourier transform increase similar. Trigonometric polynomials with frequencies only supported by hyperbolic crosses allow for a good approximation of functions of appropriate smoothness and decrease the number of used Fourier coefficients strongly. As a matter of course, an important issue is the customisation of efficient algorithms to these thinner discretisations. Sparse grids are the natural discretisations in the spatial domain. The corresponding Fourier transform suffers from stability problems. For that reason we consider sets produced by multiples of a so-called generating vector as spatial discretisations. Therewith an easy and fast evaluation of trigonometric polynomials at the grid nodes is guaranteed. Some additional assumptions ensure even stability and besides the fast reconstruction of trigonometric polynomials from the function values. We discuss necessary and sufficient conditions allowing for the stable reconstruction. 115
Page 1 and 2:
Inhaltsverzeichnis DMV Tagung 2011
Page 3 and 4:
DMV Tagung 2011 - Köln, 19. - 22.
Page 5 and 6:
DMV Tagung 2011 - Köln, 19. - 22.
Page 7 and 8:
Ken Ono Emroy University, Atlanta A
Page 9 and 10:
DMV Tagung 2011 - Köln, 19. - 22.
Page 11 and 12:
DMV Tagung 2011 - Köln, 19. - 22.
Page 13 and 14:
DMV Tagung 2011 - Köln, 19. - 22.
Page 15 and 16:
Markus Linckelmann University of Ab
Page 17 and 18:
DMV Tagung 2011 - Köln, 19. - 22.
Page 19 and 20:
Sektion 2 DMV Tagung 2011 - Köln,
Page 21 and 22:
DMV Tagung 2011 - Köln, 19. - 22.
Page 23 and 24:
Frank Kutzschebauch Universität Be
Page 25 and 26:
DMV Tagung 2011 - Köln, 19. - 22.
Page 27 and 28:
Sektion 3 Arithmetische Geometrie u
Page 29 and 30:
DMV Tagung 2011 - Köln, 19. - 22.
Page 31 and 32:
Ulrich Derenthal Ludwig-Maximilians
Page 33 and 34:
DMV Tagung 2011 - Köln, 19. - 22.
Page 35 and 36:
DMV Tagung 2011 - Köln, 19. - 22.
Page 37 and 38:
Myriam-Sonja Hantke Universität zu
Page 39 and 40:
Sektion 5 Differentialgleichungen D
Page 41 and 42:
DMV Tagung 2011 - Köln, 19. - 22.
Page 43 and 44:
DMV Tagung 2011 - Köln, 19. - 22.
Page 45 and 46:
DMV Tagung 2011 - Köln, 19. - 22.
Page 47 and 48:
Anna Dall’Acqua Otto-von-Guericke
Page 49 and 50:
André Fischer Center of Smart Inte
Page 51 and 52:
Juliette Hell Freie Universität Be
Page 53 and 54:
DMV Tagung 2011 - Köln, 19. - 22.
Page 55 and 56:
DMV Tagung 2011 - Köln, 19. - 22.
Page 57 and 58:
DMV Tagung 2011 - Köln, 19. - 22.
Page 59 and 60:
DMV Tagung 2011 - Köln, 19. - 22.
Page 61 and 62:
Felix Schulze Freie Universität Be
Page 63 and 64: Eleutherius Symeonidis Katholische
Page 65 and 66: DMV Tagung 2011 - Köln, 19. - 22.
Page 77 and 78: Sektion 8 Numerik DMV Tagung 2011 -
Page 91 and 92: Sektion 10 Geometrie und Topologie
Page 97 and 98: Felix Schlenk Universität Neuchât
Page 105 and 106: Minisymposium 2 DMV Tagung 2011 - K
Page 109 and 110: Markus Richter Karlsruher Institut
Page 113: DMV Tagung 2011 - Köln, 19. - 22.
Page 119 and 120: Minisymposium 4 DMV Tagung 2011 - K
Page 123 and 124: Edgar Brunner Universität Götting
Page 131 and 132: Minisymposium 5 Darstellungstheorie
Page 143 and 144: Jonathan Spreer Universität Stuttg
Page 155 and 156: Christian Gerhards TU Kaiserslauter
Page 165 and 166:
DMV Tagung 2011 - Köln, 19. - 22.
Page 167 and 168:
DMV Tagung 2011 - Köln, 19. - 22.
Page 169 and 170:
DMV Tagung 2011 - Köln, 19. - 22.
Page 171 and 172:
DMV Tagung 2011 - Köln, 19. - 22.
Page 173 and 174:
DMV Tagung 2011 - Köln, 19. - 22.
Page 175 and 176:
DMV Tagung 2011 - Köln, 19. - 22.
Page 177 and 178:
Minisymposium 12 Numerische Finanzm
Page 179 and 180:
DMV Tagung 2011 - Köln, 19. - 22.
Page 181 and 182:
Minisymposium 13 Operatortheorie DM
Page 183 and 184:
DMV Tagung 2011 - Köln, 19. - 22.
Page 185 and 186:
DMV Tagung 2011 - Köln, 19. - 22.
Page 187 and 188:
DMV Tagung 2011 - Köln, 19. - 22.
Page 189 and 190:
DMV Tagung 2011 - Köln, 19. - 22.
Page 191 and 192:
Minisymposium 14 DMV Tagung 2011 -
Page 193 and 194:
DMV Tagung 2011 - Köln, 19. - 22.
Page 195 and 196:
DMV Tagung 2011 - Köln, 19. - 22.
Page 197 and 198:
Minisymposium 15 Übergang Schule -
Page 199 and 200:
DMV Tagung 2011 - Köln, 19. - 22.
Page 201 and 202:
DMV Tagung 2011 - Köln, 19. - 22.
Page 203 and 204:
DMV Tagung 2011 - Köln, 19. - 22.
Page 205 and 206:
DMV Tagung 2011 - Köln, 19. - 22.
Page 207 and 208:
DMV Tagung 2011 - Köln, 19. - 22.
Page 209 and 210:
DMV Tagung 2011 - Köln, 19. - 22.
Page 211 and 212:
DMV Tagung 2011 - Köln, 19. - 22.
Page 213 and 214:
DMV Tagung 2011 - Köln, 19. - 22.
Page 215 and 216:
Autorenverzeichnis Abels, Helmut, 1
Page 217 and 218:
Martino, Maurizio, 15 Maruhn, Jan H
show all

Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?