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Publication List of Philipp Grohs
Theses
[1] P. Grohs (2010). Approximation Theory in Manifolds. Habilitation Thesis,
TU Graz. Available from http://www.sam.math.ethz.ch/~pgrohs/files/
habil.pdf.
[2] P. Grohs (2007). Smoothness analysis of nonlinear Subdivison Schemes on
regular Grids. Ph.D. thesis, TU Wien. Available from http://www.sam.
math.ethz.ch/~pgrohs/files/diss.pdf.
Books
[3] S. Dahlke, F. DeMari, P. Grohs, and D. Labate. Harmonic and
Applied Analysis – From Groups to Signals. Springer (2014), to appear.
Preprints
[4] S. Etter, P. Grohs, and A. Obermeier, FFRT – a fast finite ridgelet transform for radiative transport. Submitted. Available as
SAM Report 2014-11, ETH Z¨
urich, http://www.sam.math.ethz.ch/sam_
reports/reports_final/reports2014/2014-11.pdf.
[5] E. Fonn, P. Grohs, and R. Hiptmair, Polar spectral scheme for the
spatially homogeneous Boltzmann equation. Available as SAM Report, ETH
Z¨
urich, http://www.sam.math.ethz.ch/sam_reports/reports_final/
reports2014/2014-13.pdf.
[6] P. Grohs, S. Keiper, G. Kutyniok, and M. Schaefer, α-molecules.
Forthcoming. Available soon as SAM Report, ETH Z¨
urich, http://www.
sam.math.ethz.ch/sam_reports/reports_final/reports2014/.
[7] P. Grohs, S. Keiper, G. Kutyniok, and M. Schaefer, Cartoon approximation with α-curvelets. Submitted. Available as SAM Report 201407, ETH Z¨
urich, http://www.sam.math.ethz.ch/sam_reports/reports_
final/reports2014/2014-07.pdf.
[8] P. Grohs, Z. Kereta, and U. Wiesmann, A shearlet-based fast thresholded Landweber algorithm for deconvolution. Submitted. Preprint available
from http://www.sam.math.ethz.ch/~pgrohs/files/FTLShMAin.pdf.
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[9] P. Grohs, M. Sprecher, and T. Yu, Scattered manifold-valued data approximation. Submitted. Preprint available from http://www.sam.math.
ethz.ch/~pgrohs/files/scattered.pdf.
[10] P. Grohs and S. Hosseini, ε-subgradient algorithms for locally Lipschitz functions on Riemannian manifolds. Submitted. Available as
SAM Report 2013-49, ETH Z¨
urich, http://www.sam.math.ethz.ch/sam_
reports/reports_final/reports2013/2013-49.pdf.
[11] P. Grohs and M. Sprecher, Projection-based quasiinterpolation
in manifolds. Submitted. Available as SAM Report 2013-23, ETH
Z¨
urich, http://www.sam.math.ethz.ch/sam_reports/reports_final/
reports2013/2013-23.pdf.
[12] P. Grohs and C. Schwab, Sparse twisted tensor frame discretizations of parametric transport equations. Available as SAM Report 201141, ETH Z¨
urich, http://www.sam.math.ethz.ch/sam_reports/reports_
final/reports2011/2011-41.pdf.
[13] P. Grohs, On the maxima of cardinal refinable functions. Preprint available from http://www.sam.math.ethz.ch/~pgrohs/files/maxcard.pdf.
Journal Publications
[14] E. Fonn, P. Grohs, and R. Hiptmair, Hyperbolic cross approximation
for the spatially homogenous Boltzmann equation. IMA Journal of Numerical Analysis. In press. Preprint available from http://www.sam.math.
ethz.ch/~pgrohs/files/doc.pdf.
[15] P. Grohs, Wolfowitz’s theorem and convergence of consensus algorithms
in hadamard spaces. Proceedings of the American Mathematical Society. In
press. Preprint available from http://www.sam.math.ethz.ch/~pgrohs/
files/wolfowitz.pdf.
[16] P. Grohs, H. Hardering, and O. Sander, Optimal a priori discretization error bounds for geodesic finite elements. Foundations of Computational Mathematics. Accepted subject to minor revision. Available as
SAM Report 2013-16, ETH Z¨
urich, http://www.sam.math.ethz.ch/sam_
reports/reports_final/reports2013/2013-16.pdf.
[17] P. Grohs and G. Kutyniok, Parabolic molecules. Foundations of Computational Mathematics. In Press. DOI: http://dx.doi.org/10.1007/
s10208-013-9170-z.
[18] P. Grohs and S. Vigogna, Intrinsic localization of anisotropic frames
II: α-molecules. Journal of Fourier Analysis and Applications. Accepted
subject to revision. Preprint available from http://www.sam.math.ethz.
ch/~pgrohs/files/loc2.pdf.
[19] P. Grohs, Bandlimited shearlet-type frames with nice duals. Journal of
Computational and Applied Mathematics, 243, (2013), 139 – 151. DOI:
http://dx.doi.org/10.1016/j.cam.2012.10.030.
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[20] P. Grohs, Geometric multiscale decompositions of dynamic low-rank matrices. Computer Aided Geometric Design, 30, (2013), 805–826. DOI:
http://dx.doi.org/10.1016/j.cagd.2013.07.002.
[21] P. Grohs, Intrinsic localization of anisotropic frames. Applied and Computational Harmonic Analysis, 35, (2013), 264–283. DOI: http://dx.doi.
org/10.1016/j.acha.2012.09.003.
[22] P. Grohs, Quasiinterpolation for Riemannian data. IMA Journal of Numerical Analysis, 33, (2013), 849–874. DOI: http://dx.doi.org/10.
1093/imanum/drs026.
[23] P. Grohs, Refinable functions for dilation families. Advances in Computational Mathematics, 38, (2013), 531–561. DOI: http://dx.doi.org/10.
1007/s10444-011-9248-6.
[24] P. Grohs, Ridgelet-type frame decompositions for Sobolev spaces related to
linear transport. Journal of Fourier Analysis and Applications, 18, (2012),
309–325. DOI: http://dx.doi.org/10.1007/s00041-011-9206-1.
[25] P. Grohs, Tree approximation with anisotropic decompositions. Applied
and Computational Harmonic Analysis, 33, (2012), 44–57. DOI: http:
//dx.doi.org/10.1016/j.acha.2011.09.004.
[26] P. Grohs and J. Wallner, Definability and stability of multiscale decompositions for manifold-valued data. Journal of the Franklin Institute, 349(5), (2012), 1648–1664. DOI: http://dx.doi.org/10.1016/j.
jfranklin.2011.02.010.
[27] M. Skopenkov, H. Pottmann, and P. Grohs, Ruled Laguerre minimal
surfaces. Mathematische Zeitschrift, 272(1), (2012), 646–674. DOI: http:
//dx.doi.org/10.1007/s00209-011-0953-0.
[28] P. Grohs, Continuous Shearlet Frames and Resolution of the Wavefront
Set. Monatshefte f¨
ur Mathematik, 164(4), (2011), 393–426. DOI: http:
//dx.doi.org/10.1007/s00605-010-0264-2.
[29] P. Grohs, Continuous shearlet tight frames. Journal of Fourier Analysis
and Applications, 17(3), (2011), 506–518. DOI: http://dx.doi.org/10.
1007/s00041-010-9149-y.
[30] N. Dyn, P. Grohs, and J. Wallner, Approximation order of interpolatory nonlinear subdivision schemes. Journal of Computational and Applied
Mathematics, 233(7), (2010), 1697–1703. DOI: http://dx.doi.org/10.
1016/j.cam.2009.02.017.
[31] P. Grohs, Approximation order from stability of nonlinear subdivision
schemes. Journal of Approximation Theory, 162, (2010), 1085–1094. DOI:
http://dx.doi.org/10.1016/j.jat.2009.12.003.
[32] P. Grohs, A general proximity analysis of nonlinear subdivision schemes.
SIAM Journal on Mathematical Analysis, 42, (2010), 729–750. DOI: http:
//dx.doi.org/10.1137/09075963X.
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[33] P. Grohs, Stability of manifold-valued subdivision schemes and multiscale
transformations. Constructive Approximation, 32, (2010), 569–596. DOI:
http://dx.doi.org/10.1007/s00365-010-9085-8.
[34] H. Pottmann, P. Grohs, and B. Blaschitz, Edge offset meshes in
Laguerre geometry. Advances in Computational Mathematics, 33, (2010),
45–73. DOI: http://dx.doi.org/10.1007/s10444-009-9119-6.
[35] P. Grohs, Smoothness equivalence properties of univariate subdivision schemes and their projection analogues.
Numerische Mathematik, 113(2), (2009), 163–180. DOI: http://dx.doi.org/10.1007/
s00211-009-0231-9.
[36] P. Grohs, Smoothness of interpolatory multivariate subdivision in Lie
groups. IMA Journal of Numerical Analysis, 29, (2009), 760–772. DOI:
http://dx.doi.org/10.1093/imanum/drn040.
[37] P. Grohs and J. Wallner, Interpolatory wavelets for manifold-valued
data. Applied and Computational Harmonic Analysis, 27(3), (2009), 325–
333. DOI: http://dx.doi.org/10.1016/j.acha.2009.05.005.
[38] H. Pottmann, P. Grohs, and N. Mitra, Laguerre minimal surfaces, isotropic geometry and linear elasticity. Advances in Computational
Mathematics, 31, (2009), 391–419. DOI: http://dx.doi.org/10.1007/
s10444-008-9076-5.
[39] P. Grohs, Smoothness analysis of subdivision schemes on regular grids by
proximity. SIAM Journal on Numerical Analysis, 46(4), (2008), 2169. DOI:
http://dx.doi.org/10.1137/060669759.
[40] J. Wallner, E. Navayazdani, and P. Grohs, Smoothness properties
of Lie group subdivision schemes. Multiscale Modeling and Simulation, 6,
(2007), 493–505. DOI: http://dx.doi.org/10.1137/060668353.
Refereed Conference Proceedings
[41] P. Grohs, S. Keiper, G. Kutyniok, and M. Schaefer (2014).
Parabolic molecules: Curvelets, shearlets and beyond. In G. Fasshauer
and L. L. Schumaker (editors), Approximation Theory XIV: San Antonio 2013. Springer. Preprint available from http://www.sam.math.ethz.
ch/~pgrohs/files/ParaOver.pdf.
[42] P. Grohs, S. Keiper, G. Kutyniok, and M. Schaefer (2013). αmolecules: Curvelets, shearlets, ridgelets, and beyond. In Proceedings SPIE
2013. Preprint available from http://www.sam.math.ethz.ch/~pgrohs/
files/AlphaSPIE.pdf.
[43] P. Grohs (2011). Tree approximation and optimal image coding with shearlets. In SampTA (Sampling Theory and Applications): Singapore 2011.
Preprint available from http://www.sam.math.ethz.ch/~pgrohs/files/
SampTA_Grohs.pdf.
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[44] P. Grohs (2010). Interpolating composite systems. In M. Neamtu
and L. L. Schumaker (editors), Approximation Theory XIII: San
Antonio 2010. Nashboro Press. DOI: http://dx.doi.org/10.1007/
978-1-4614-0772-08.
[45] P. Grohs and J. Wallner (2008). Log-exponential analogues of univariate subdivision schemes in Lie groups and their smoothness properties.
In M. Neamtu and L. L. Schumaker (editors), Approximation Theory
XII: San Antonio 2007, pages 181–190. Nashboro Press. Preprint available
from http://www.sam.math.ethz.ch/~pgrohs/files/grvar.pdf.
Book Chapters
[46] P. Grohs (2012). Shearlets and microlocal analysis. In Shearlets: Multiscale Analysis for Multivariate Data. Birkh¨auser Springer. DOI: http:
//dx.doi.org/10.1007/978-0-8176-8316-0_2.
Others
[47] P. Grohs (2012). On the structure of anisotropic frames. Oberwolfach
Report 29. DOI: http://dx.doi.org/10.4171/OWR/2012/29.
[48] P. Grohs (2010). Book Review: Invitation to Ergodic Theory by C. Silva
(AMS 2008). Internationale Mathematische Nachrichten, 211, 2009. Available from http://www.oemg.ac.at/IMN/imn211.pdf.
[49] P. Grohs (2010). The continuous shearlet transform: Representation
formulae and microlocal analysis. Oberwolfach Report 44. DOI: http:
//dx.doi.org/10.4171/OWR/2010/44.
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