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2. Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms.

Author

Hangelbroek, T. and Rieger, C.

Subjects
*INTERPOLATION spaces, *RADIAL basis functions, *HILBERT space, *INTERPOLATION, *MATHEMATICS
Abstract

Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal rates for the whole RKHS are often known. Schaback added the doubling trick [Math. Comp. 68 (1999), pp. 201–216], which shows that functions having double the smoothness required by the RKHS (along with specific, albeit complicated boundary behavior) can be approximated with higher convergence rates than the optimal rates for the whole space. Other advances allowed interpolation of target functions which are less smooth, and different norms which measure interpolation error. The current state of the art of error analysis for RBF interpolation treats target functions having smoothness up to twice that of the native space, but error measured in norms which are weaker than that required for membership in the RKHS. Motivated by the fact that the kernels and the approximants they generate are smoother than required by the native space, this article extends the doubling trick to error which measures higher smoothness. This extension holds for a family of kernels satisfying easily checked hypotheses which we describe in this article, and includes many prominent RBFs. In the course of the proof, new convergence rates are obtained for the abstract operator considered by Devore and Ron in [Trans. Amer. Math. Soc. 362 (2010), pp. 6205–6229], and new Bernstein estimates are obtained relating high order smoothness norms to the native space norm. [ABSTRACT FROM AUTHOR]

Published
2025
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5. Theranostics in chemotherapy resistant MIBC by instillation of FAP & CXCR4 radioligands into the bladder - the Bladder BRIDGister experience

Author

Wirtz, R., primary, Kastner, L., additional, Friedersdorff, F., additional, Schlomm, T., additional, Barski, D., additional, Otto, T., additional, Waldner, M., additional, Graff, J., additional, Veltrup, E., additional, Linden, F., additional, Schwandt, M., additional, Hake, R., additional, Eidt, S., additional, Roggisch, J., additional, Rieger, C., additional, Koch, S., additional, Klatte, T., additional, Ecke, T., additional, Heidenreich, A., additional, Greifenstein, L., additional, and Baum, R.P., additional

Published
2024
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6. Why underrepresentation costs lives: Results from a high-volume multi-institutional study about risk factors for mortality in Fournier's gangrene

Author

Rieger, C, Hübers, M, Pfister, D, Storz, E, Schleifer, S, Kranz, J, Gerdes, B, Pantea, V, Püllen, L, Chachin, A, Träger, M, Henniges, P, Vetterlein, M, Klemm, J, Roghmann, F, Dellino, M, Jany, U, Tylingr, M, Al Assali, K, Patroi, P, Mayr, R, Engelmann, S, Schneidewind, L, Zengerling, F, Heidenreich, A, Rieger, C, Hübers, M, Pfister, D, Storz, E, Schleifer, S, Kranz, J, Gerdes, B, Pantea, V, Püllen, L, Chachin, A, Träger, M, Henniges, P, Vetterlein, M, Klemm, J, Roghmann, F, Dellino, M, Jany, U, Tylingr, M, Al Assali, K, Patroi, P, Mayr, R, Engelmann, S, Schneidewind, L, Zengerling, F, and Heidenreich, A

Published
2024

8. First proof-of-concept of theranostic instillation therapy for muscle invasive bladder cancer patients within the Bladder BRIDGister study group

Author

Barski, D, Wirtz, R, Kastner, L, Voß, PC, Friedersdorff, F, Otto, T, Waldner, M, Veltrup, E, Linden, F, Hake, R, Eidt, S, Roggisch, J, Rieger, C, Koch, S, Ecke, T, Heidenreich, A, Greifenstein, L, Baum, RP, Barski, D, Wirtz, R, Kastner, L, Voß, PC, Friedersdorff, F, Otto, T, Waldner, M, Veltrup, E, Linden, F, Hake, R, Eidt, S, Roggisch, J, Rieger, C, Koch, S, Ecke, T, Heidenreich, A, Greifenstein, L, and Baum, RP

Published
2024

21. Infektiöse und obstruktive Krankheiten des Respirationstraktes

Author

Nadal, D., Seidenberg, J., Forster, J., Rieger, C., Paul, K., Riedel, F., Szczepanski, R., Thal, W., von der Hardt, H., Skopnik, H., Wenzl, T. G., Freihorst, J., Götz, M., Roesler, J., Bienzle, U., Frischer, T., Magdorf, K., Rieger, C., editor, von der Hardt, H., editor, Sennhauser, F. H., editor, Wahn, U., editor, and Zach, M., editor

Published
2004
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22. Der gesunde Respirationstrakt

Author

Tschanz, S. A., Burri, P. H., Schittny, J. C., Poets, C. F., Nicolai, T., Hammer, J., Zach, M., Riedler, J., Böning, D., Hütler, M., Griese, M., Kummer, W., Hahn, H. L., Pabst, R., Tschernig, T., Rieger, C., Schroten, H., Renz, H., Im Hof, V., Gehr, P., Wildhaber, J. H., Rieger, C., editor, von der Hardt, H., editor, Sennhauser, F. H., editor, Wahn, U., editor, and Zach, M., editor

Published
2004
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25. Influenza virus infections in patients with malignancies –– characteristics and outcome of the season 2014/15. A survey conducted by the Infectious Diseases Working Party (AGIHO) of the German Society of Haematology and Medical Oncology (DGHO)

Author

Hermann, B., Lehners, N., Brodhun, M., Boden, K., Hochhaus, A., Kochanek, M., Meckel, K., Mayer, K., Rachow, T., Rieger, C., Schalk, E., Weber, T., Schmeier-Jürchott, A., Schlattmann, P., Teschner, D., and von Lilienfeld-Toal, M.

Published
2017
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28. Infektiöse und obstruktive Krankheiten des Respirationstraktes

Author

Nadal, D., Seidenberg, J., Forster, J., Rieger, C., Paul, K., Riedel, F., Szczepanski, R., Thal, W., von der Hardt, H., Skopnik, H., Wenzl, T. G., Freihorst, J., Götz, M., Roesler, J., Bienzle, U., Frischer, T., Magdorf, K., Rieger, C., editor, von der Hardt, H., editor, Sennhauser, F. H., editor, Wahn, U., editor, and Zach, M., editor

Published
1999
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30. Der gesunde Respirationstrakt

Author

Tschanz, S. A., Burri, P. H., Schittny, J. C., Poets, C. F., Nicolai, T., Hammer, J., Zach, M., Riedler, J., Böning, D., Hütler, M., Griese, M., Kummer, W., Hahn, H. L., Pabst, R., Tschernig, T., Rieger, C., Schroten, H., Renz, H., Hof, V. Im, Gehr, P., Kusenbach, G., Rieger, C., editor, von der Hardt, H., editor, Sennhauser, F. H., editor, Wahn, U., editor, and Zach, M., editor

Published
1999
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33. Vaskulitiden

Author

Rieger, C., Lentze, Michael J., editor, Schulte, Franz J., editor, Schaub, Jürgen, editor, and Spranger, Jürgen, editor

Published
2007
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38. Vaskulitiden

Author

Rieger, C., Lentze, Michael J., editor, Schulte, Franz J., editor, Schaub, Jürgen, editor, and Spranger, Jürgen, editor

Published
2003
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39. Krankheiten der Atmungsorgane

Author

Burri, P. H., Poets, C. F., Hammer, J., Frey, U., Rieger, C., Fanconi, S., Fischer, J., Riedler, J., Rutishauser, M., Zach, M. S., Waag, K. L., von der Hardt, H., Forster, H., Heininger, U., Kusenbach, G., Freihorst, J., Schöni, M. H., Sennhauser, F. H., Wildhaber, J. H., Götz, M., Henker, J., Thies, W.-R., Meyer, H., Christiansen, H., Lampert, F., Sacher, P., Nicolai, T., Thal, W., von Mutius, E., Seidenberg, J., Riedel, F., Frischer, T., Lemburg, P., Oberwaldner, B., Bauer, C. P., Lentze, Michael J., editor, Schaub, Jürgen, editor, Schulte, Franz J., editor, and Spranger, Jürgen, editor

Published
2001
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40. Autoimmunkrankheiten

Author

Dannecker, G., Habermehl, P., Zepp, E., Ganser, G., Huppertz, H.-I., Wagner, N., Rieger, C., Michels, H., Truckenbrodt, H., Lentze, Michael J., editor, Schaub, Jürgen, editor, Schulte, Franz J., editor, and Spranger, Jürgen, editor

Published
2001
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48. What's new in diagnosis and antimicrobial therapy of febrile neutropenic patients with lung infiltrates?

Author

Rieger, C., Barlow, S., and Maschmeyer, G.

Subjects
Care and treatment, Diagnostic imaging, Posaconazole, Palliative care, Pentamidine, Caspofungin, Methicillin, Pentamidine isethionate, Palliative treatment
Abstract

Author(s): C. Rieger [sup.1], S. Barlow [sup.1], G. Maschmeyer [sup.2] Author Affiliations: (1) grid.5252.0, 000000041936973X, Department of Hematology and Oncology, Ludwig-Maximilians-University Munich, , Munich, Germany (2) grid.419816.3, 0000000403903563, Department of [...]

Published
2014
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