Person ::

Sommer, Prof. Dr. Manfred

2019

• 

  

  Sommer, Manfred:
  Property A and best L^1-Approximation.
  In: Dolomites research notes on approximation. 12 (2019). - S. 29-37.
  ISSN 2035-6803
  10.14658/pupj-drna-2019-Special_Issue-5
  (Peer-Review-Journal)

2012

• 

  Sommer, Manfred:
  On the Chebyshev rank of multivariate splines in L^1-approximation.
  In: Journal of approximation theory. 164 (2012) 11. - S. 1472-1495.
  ISSN 0021-9045
  (Peer-Review-Journal)

2010

• Sommer, Manfred:
  The Chebyshev rank of multivariate polynomials in L1-approximation.
  In: Journal of approximation theory. 162 (2010).
  ISSN 0021-9045
  (Peer-Review-Journal)

2009

• Actual problems of control theory, topology and operator equations : International Jubilee Conference at the Kyrgyz-Russian Slavic University Bishkek, Kyrgyzstan, September 15 - 21, 2008.
  Hrsg.: Grothmann, René ; Lelevkina, Liliya G. ; Sommer, Manfred
  Aachen : Shaker, 2009. - XVI, 203 S. - (Mathematics)
  ISBN 978-3-8322-8367-4
• 

  Grothmann, René ; Sommer, Manfred:
  Composing circular arcs with minimal NURBS.
  In: International mathematical forum. 4 (2009) 5-8. - S. 193-218.
  ISSN 1312-7594
  (Peer-Review-Journal)
• Sommer, Manfred:
  Interpolation by spline functions.
  In: Grothmann, René [Hrsg.]: Actual problems of control theory, topology and operator equations : international jubilee conference at the Kyrgyz-Russian Slavic University Bishkek, Kyrgyzstan, September 15 - 21, 2008. - Aachen : Shaker, 2009. - S. 185-203. - (Mathematics)
  ISBN 978-3-8322-8367-4

2007

• Sommer, Manfred:
  Some remarks on minimal spline interpolation.
  In: Applied mathematical sciences. 1 (2007). - S. 1265-1276.
  ISSN 1312-885x
  (Peer-Review-Journal)

2006

• Sommer, Manfred:
  Hermite interpolation of data sets by minimal spline spaces.
  In: Constructive approximation. 23 (2006). - S. 211-227.
  ISSN 0176-4276 ; 1432-0940
  (Peer-Review-Journal)
• Sommer, Manfred:
  Interpolation by uni- and multivariate spline functions.
  In: Program Systems : theory and application (Proceedings of an International Conference in Pereslavl-Zalessky, Russia). - Pereslavl-Zalessky, 2006. - S. 337-352
  ISBN 5-94052-127-4

2005

• Sommer, Manfred:
  Characterization of periodic L1-unicity subspaces.
  In: Constructive approximation. 21/22 (2005). - S. 95-112.
  ISSN 0176-4276 ; 1432-0940
  (Peer-Review-Journal)
• Sommer, Manfred:
  On the Chebyshev rank of differentiable bivariate splines in L1-approximation.
  In: International journal of pure and applied mathematics. 23 (2005). - S. 479-490.
  ISSN 1311-8080
  (Peer-Review-Journal)
• Sommer, Manfred:
  On the Chebyshev rank of bivariate polynomials and splines in L1-approximation.
  In: International journal of pure and applied mathematics. 18 (2005). - S. 503-533.
  ISSN 1311-8080
  (Peer-Review-Journal)

2003

• Analytical and Approximate Methods : International Conference at the Kyrgyz-Russian-Slavic University Bishkek, Kyrgyzstan, September 23-24, 2002.
  Hrsg.: Blatt, Hans-Peter ; Felix, Rainer ; Lelevkina, Liliya G. ; Sommer, Manfred
  Aachen : Shaker, 2003. - XI, 233 S.
  ISBN 3-8322-2147-6
• 

  Sommer, Manfred:
  Uniqueness of periodic best L^1-approximations.
  In: Journal of approximation theory. 123 (2003) 1. - S. 89-109.
  ISSN 0021-9045
  (Peer-Review-Journal)
• Sommer, Manfred:
  On best approximation of continuous functions.
  In: Blatt, Hans-Peter ; Felix, Rainer ; Lelevkina, Liliya G. ; Sommer, Manfred (Hrsg.): Analytical and Approximate Methods : international conference at the Kyrgyz-Russian-Slavic University Bishkek, Kyrgyzstan, September 23 - 24, 2002. - Aachen : Shaker, 2003. - S. 221-233
  ISBN 3-8322-2147-6

2000

• 

  Davydov, Oleg ; Sommer, Manfred:
  Interpolation by weak Chebyshev spaces.
  In: Journal of approximation theory. 102 (2000) 2. - S. 243-262.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Davydov, Oleg ; Sommer, Manfred ; Strauß, Hans:
  Interpolation by bivariate linear splines.
  In: Journal of computational and applied mathematics. 119 (2000) 1-2. - S. 115-131.
  ISSN 0771-050x ; 0377-0427
  (Peer-Review-Journal)

1999

• Davydov, Oleg ; Sommer, Manfred ; Strauß, Hans:
  On almost interpolation and locally linearly independent bases.
  In: East journal on approximations. 5 (1999) 1. - S. 67-88.
  ISSN 1310-6236
  (Peer-Review-Journal)

1998

• Davydov, Oleg ; Sommer, Manfred:
  Interpolation and almost interpolation by weak Chebyshev spaces.
  In: Chui, Charles K. ; Schumaker, Larry L. (Hrsg.): Approximation Theory IX. - Nashville : Vanderbuilt University Press, 1998. - S. 25-32. - (Innovations in applied mathematics)
  ISBN 0-8265-1327-1

1997

• Davydov, Oleg ; Sommer, Manfred ; Strauß, Hans:
  On almost interpolation by multivariate splines.
  In: Nürnberger, Günther ; Schmidt, Jochen W. ; Walz, Guido (Hrsg.): Multivariate Approximation and Splines. - Basel : Birkhäuser, 1997. - S. 45-58. - (International Series of Numerical Mathematics ; 125)
  ISBN 3-7643-5654-5 ; 0-8176-5654-5
• Davydov, Oleg ; Sommer, Manfred ; Strauß, Hans:
  Locally linearly independent systems and almost interpolation.
  In: Nürnberger, Günther ; Schmidt, Jochen W. ; Walz, Guido (Hrsg.): Multivariate Approximation and Splines. - Basel : Birkhäuser, 1997. - S. 59-72. - (International Series of Numerical Mathematics ; 125)
  ISBN 3-7643-5654-5 ; 0-8176-5654-5

1996

• Sommer, Manfred ; Strauß, Hans:
  A condition of Schoenberg-Whitney type for multivariate spline interpolation.
  In: Advances in the theory of computation and computational mathematics : ATCCM. 1 (1996) 5. - S. 381-397.
• Sommer, Manfred ; Strauß, Hans:
  Totally positive systems and interpolation by subspaces of generalized splines.
  In: Gasca, Mariano ; Micchelli, Charles A. (Hrsg.): Total Positivity and its Applications. - Dordrecht : Kluwer, 1996. - S. 85-94. - (Mathematics and its applications ; 359)
  ISBN 0-7923-3924-X

1995

• 

  Sommer, Manfred ; Strauß, Hans:
  Interpolation by uni- and multivariate generalized splines.
  In: Journal of approximation theory. 83 (1995) 3. - S. 423-447.
  ISSN 0021-9045
  (Peer-Review-Journal)

1993

• 

  Sommer, Manfred ; Strauß, Hans:
  Order of strong uniqueness in best L∞-approximation by spline spaces.
  In: Acta mathematica Hungarica. 61 (1993) 3-4. - S. 259-280.
  ISSN 0001-5954 ; 0236-5294
  10.1007/bf01874685
  (Peer-Review-Journal)
• Grötzbach, Erwin ; Sommer, Manfred:
  Mathematisch-Geographische Fakultät 1980 bis 1993.
  In: Müller, Rainer A. (Hrsg.): Veritati et Vitae : Festschrift / im Auftrag der Geschichts- und Gesellschaftswissenschaftlichen Fakultät der Katholischen Universität Eichstätt. Band 2., Vom Bischöflichen Lyzeum zur Katholischen Universität. - Regensburg : Pustet, 1993. - S. 268-274. - (Eichstätter Studien / Neue Folge ; 33,2)
  ISBN 3-7917-1376-0

1992

• 

  Kroó, András ; Schmidt, Darrell ; Sommer, Manfred:
  On A-spaces and their relation to the Hobby-Rice theorem.
  In: Journal of approximation theory. 68 (1992) 2. - S. 136-154.
  ISSN 0021-9045
  (Peer-Review-Journal)
• Sommer, Manfred:
  Segment approximation using linear functionals.
  In: Braess, Dietrich ; Schumaker, Larry L.: (Hrsg.): Numerical Methods of Approximation Theory. Vol. 9. Proceedings of a Conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungsinstitut in Oberwolfach during the week of November 24 - 30, 1991. - Basel : Birkhäuser, 1992. - S. 331-346. - (International Series of Numerical Mathematics ; 105)
  ISBN 3-7643-2746-4 ; 0-8176-2746-4

1991

• 

  Kroó, András ; Schmidt, Darrell ; Sommer, Manfred:
  Some properties of A-spaces and their relationship to L^1-approximation.
  In: Constructive approximation. 7 (1991) 1. - S. 329-339.
  ISSN 0176-4276 ; 1432-0940
  (Peer-Review-Journal)
• Sommer, Manfred:
  Über eine Rechnerarithmetik mit Ergebnisverifikation.
  In: 7. Eichstätter Kolloquium zur Didaktik der Mathematik : 21. Februar 1991. - Eichstätt : Katholische Universität Eichstätt, Mathematisch-Geographische Fakultät, 1991. - S. 1-16

1989

• 

  Sommer, Manfred ; Strauß, Hans:
  Chebyshev rank in one-sided L^1-approximation.
  In: Approximation theory and its applications : ATA. 5 (1989) 4. - S. 79-94.
  ISSN 1000-9221
  (Peer-Review-Journal)
• 

  Sommer, Manfred ; Strauß, Hans:
  A characterization of Descartes systems in Haar subspaces.
  In: Journal of approximation theory. 57 (1989) 1. - S. 104-116.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Nürnberger, Günther ; Schumaker, Larry L. ; Sommer, Manfred ; Strauß, Hans:
  Uniform approximation by generalized splines with free knots.
  In: Journal of approximation theory. 59 (1989) 2. - S. 150-169.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Meinardus, Günter ; Nürnberger, Günther ; Sommer, Manfred ; Strauß, Hans:
  Algorithms for piecewise polynomials and splines with free knots.
  In: Mathematics of computation. 53 (1989) 187. - S. 235-247.
  ISSN 0025-5718
  (Peer-Review-Journal)
• 

  Kroó, András ; Sommer, Manfred ; Strauß, Hans:
  On strong uniqueness in one-sided L^1-approximation of differentiable functions.
  In: Proceedings of the American Mathematical Society. 106 (1989) 4. - S. 1011-1016.
  ISSN 0002-9939 ; 1088-6826
  (Peer-Review-Journal)
• Sommer, Manfred:
  Chebyshev rank of bivariate polynomials in L^1-approximation.
  In: Chui, Charles, K. ; Schumaker, Larry L. ; Ward, J. D. (Hrsg.): Approximation Theory VI : proceedings of the Sixth International Symposium on Approximation Theory, held at Texas A & M University on January 9-13, 1989. - Boston : Academic Press, 1989. - S. 597-600
  ISBN 0-12-174586-4 ; 0-12-174587-2

1988

• 

  Sommer, Manfred ; Strauß, Hans:
  Weak Descartes systems in generalized spline spaces.
  In: Constructive approximation. 4 (1988) 1. - S. 133-145.
  ISSN 0176-4276 ; 1432-0940
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Properties of unicity subspaces in L_1-approximation.
  In: Journal of approximation theory. 52 (1988) 3. - S. 269-283.
  ISSN 0021-9045
  (Peer-Review-Journal)
• Sommer, Manfred ; Strauß, Hans:
  Descartes systems in Haar subspaces.
  In: Sendov, Blagovest Ch. ; Petrushev, P. ; Ivanov, K. ; Maleev, R. (Hrsg.): Constructive Theory of Functions : proceedings of the International Conference on Constructive Theory of Functions, Varna, May 24 - May 31, 1987. - Sofia : Publishing House of the Bulgarian Academy of Sciences, 1988. - S. 428-432

1987

• 

  Sommer, Manfred:
  Examples of unicity subspaces in L_1-approximation.
  In: Numerical functional analysis and optimization. 9 (1987) 1-2. - S. 131-146.
  ISSN 0163-0563
  (Peer-Review-Journal)

1986

• 

  Nürnberger, Günther ; Sommer, Manfred ; Strauß, Hans:
  An algorithm for segment approximation.
  In: Numerische Mathematik. 48 (1986) 4. - S. 463-477.
  ISSN 0029-599x
  (Peer-Review-Journal)
• Sommer, Manfred:
  Some properties of unicity subspaces in L_1-approximation.
  In: Chui, Charles K. ; Schumaker, Larry L. ; Ward, Joseph D. (Hrsg.): Approximation Theory V : proceedings of the Fifth International Symposium on Approximation Theory, held at Texas A and M University on January 13 - 17, 1986. - Boston : Academic Press, 1986. - S. 563-566
  ISBN 0-12-174581-3

1985

• 

  Nürnberger, Günther ; Schumaker, Larry L. ; Sommer, Manfred ; Strauß, Hans:
  Approximation by generalized splines.
  In: Journal of mathematical analysis and applications. 108 (1985) 2. - S. 466-494.
  ISSN 0022-247x ; 1096-0813
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Parametric approximation by splines.
  In: Numerical functional analysis and optimization. 7 (1985) 1. - S. 1-21.
  ISSN 0163-0563
  (Peer-Review-Journal)
• Sommer, Manfred ; Nürnberger, Günther:
  Continuous selections in Chebyshev approximation.
  In: Brosowski, Bruno ; Deutsch, Frank (Hrsg.): Parametric Optimization and Approximation : conference held at the Mathematisches Forschungsinstitut Oberwolfach, October 16 - 22, 1983. - Basel : Birkhäuser, 1985. - S. 248-263. - (International Series of Numerical Mathematics ; 72)
  ISBN 3-7643-1671-3
• Sommer, Manfred:
  Uniqueness of best L_1-approximations of continuous functions.
  In: Meinardus, Günter ; Nürnberger Günther (Hrsg.): Delay Equations, Approximation and Application : International Symposium at the University of Mannheim, October 8–11, 1984. - Basel u.a. : Birkhäuser, 1985. - S. 264-281. - (International Series of Numerical Mathematics ; 74)
  ISBN 3-7643-1733-7

1984

• 

  Nürnberger, Günther ; Schumaker, Larry L. ; Sommer, Manfred ; Strauß, Hans:
  Generalized Tchebycheffian splines.
  In: SIAM journal on mathematical analysis. 15 (1984) 4. - S. 790-804.
  ISSN 0036-1410 ; 1095-7154
  (Peer-Review-Journal)
• Sommer, Manfred:
  Convergence of best L_p-approximations in subspaces of spline functions.
  In: Chui, Charles K. ; Schumaker, Larry L. ; Ward, Joseph D. (Hrsg.): Approximation Theory IV : proceedings of the International Symposium on Approximation Theory, held at Texas A&M University, College Station, Texas, on January 10 - 14, 1983. - New York u.a. : Academic Press, 1984. - S. 685-690
  ISBN 0-12-174580-5

1983

• 

  Sommer, Manfred:
  Weak Chebyshev spaces and best L_1-approximation.
  In: Journal of approximation theory. 39 (1983) 1. - S. 54-71.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Continuous selections and convergence of best L_p-approximations in subspaces of spline functions.
  In: Numerical functional analysis and optimization. 6 (1983) 2. - S. 212-234.
  ISSN 0163-0563
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Some results on best L_1-approximation of continuous functions.
  In: Numerical functional analysis and optimization. 6 (1983) 3. - S. 253-271.
  ISSN 0163-0563
  (Peer-Review-Journal)
• 

  Nürnberger, Günther ; Sommer, Manfred:
  A Remez type algorithm for spline functions.
  In: Numerische Mathematik. 41 (1983) 1. - S. 117-146.
  ISSN 0029-599x
  (Peer-Review-Journal)
• 

  Nürnberger, Günther ; Schumaker, Larry L. ; Sommer, Manfred ; Strauß, Hans:
  Interpolation by generalized splines.
  In: Numerische Mathematik. 42 (1983) 2. - S. 195-212.
  ISSN 0029-599x
  (Peer-Review-Journal)
• 

  Nürnberger, Günther ; Sommer, Manfred:
  Alternation for best spline approximations.
  In: Numerische Mathematik. 41 (1983) 2. - S. 207-221.
  ISSN 0029-599x
  (Peer-Review-Journal)
• Sommer, Manfred:
  L_p-approximations and Chebyshev approximations in subspaces of spline functions.
  In: Brosowski, Bruno ; Martensen, Erich (Hrsg.): Approximation and optimization in mathematical physics : papers presented to the 10th Conference on Methoden und Verfahren der Mathematischen Physik, held on February 21 - 27, 1982 at the Mathematisches Forschungsinstitut Oberwolfach. - Frankfurt am Main : Lang, 1983. - S. 105-139. - (Methoden und Verfahren der mathematischen Physik ; 27)
  ISBN 3-8204-7631-8

1982

• 

  Sommer, Manfred:
  Existence of pointwise-Lipschitz-continuous selections of the metric projection for a class of Z-spaces.
  In: Journal of approximation theory. 34 (1982) 2. - S. 115-130.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Finite dimensional subspaces and alternation.
  In: Journal of approximation theory. 34 (1982) 2. - S. 131-145.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Sommer, Manfred ; Strauß, Hans:
  Unicity of best one-sided L_1-approximations for certain classes of spline functions.
  In: Numerical functional analysis and optimization. 4 (1982) 4. - S. 413-435.
  ISSN 0163-0563
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Characterization of continuous selections of the metric projection for a class of weak Chebyshev spaces.
  In: SIAM journal on mathematical analysis. 13 (1982) 2. - S. 280-294.
  ISSN 0036-1410 ; 1095-7154
  (Peer-Review-Journal)

1981

• Blatt, Hans-Peter ; Nürnberger, Günther ; Sommer, Manfred:
  A characterization of pointwise-Lipschitz-continuous selections for the metric projection.
  In: Numerical functional analysis and optimization. 4 (1981). - S. 101-121.
  ISSN 0163-0563
  (Peer-Review-Journal)

1980

• 

  Sommer, Manfred:
  Characterization of continuous selections for the metric projection for generalized splines.
  In: SIAM journal on mathematical analysis. 11 (1980) 1. - S. 23-40.
  ISSN 0036-1410 ; 1095-7154
  (Peer-Review-Journal)
• 

  Sommer, Manfred:
  Nonexistence of continuous selections of the metric projection for a class of weak Chebyshev spaces.
  In: Transactions of the American Mathematical Society. 260 (1980). - S. 403-409.
  ISSN 0002-9947
  (Peer-Review-Journal)
• Blatt, Hans-Peter ; Nürnberger, Günther ; Sommer, Manfred:
  Pointwise-Lipschitz-continuous selections for the metric projection.
  In: Cheney, Elliot W. (Hrsg.): Approximation Theory III : proceedings of a Conference Honoring Professor George G. Lorentz, held at the University of Texas at Austin January 8 - 12, 1980. - New York : Academic Press, 1980. - S. 223-228
  ISBN 0-12-171050-5
• Sommer, Manfred:
  Continuous selections for metric projections.
  In: Devore, Ronald A. ; Scherer, Karl (Hrsg.): Quantitative Approximation : proceedings of a Symposium held in Bonn, West germany, August 20 - 24, 1979. - New York : Academic Press, 1980. - S. 301-317
  ISBN 0-12-213650-0

1979

• 

  Sommer, Manfred:
  Continuous selections of the metric projection for 1-Chebyshev spaces.
  In: Journal of approximation theory. 26 (1979) 1. - S. 46-53.
  ISSN 0021-9045
  (Peer-Review-Journal)
• Sommer, Manfred:
  L_1-approximation by weak Chebyshev spaces.
  In: Meinardus, Günter (Hrsg.): Approximation in Theorie und Praxis : ein Symposiumsbericht. - Mannheim u.a. : Bibliographisches Institut, 1979. - S. 85-102
  ISBN 3-411-01567-5

1978

• 

  Nürnberger, Günther ; Sommer, Manfred:
  Characterization of continuous selections of the metric projection for spline functions.
  In: Journal of approximation theory. 22 (1978) 4. - S. 320-330.
  ISSN 0021-9045
  (Peer-Review-Journal)
• 

  Nürnberger, Günther ; Sommer, Manfred:
  Weak Chebyshev subspaces and continuous selections for the metric projection.
  In: Transactions of the American Mathematical Society. 238 (1978). - S. 129-138.
  ISSN 0002-9947
  (Peer-Review-Journal)

1977

• 

  Sommer, Manfred ; Strauß, Hans:
  Eigenschaften von schwach tschebyscheffschen Räumen.
  In: Journal of approximation theory. 21 (1977) 3. - S. 257-268.
  ISSN 0021-9045
  (Peer-Review-Journal)

1976

• Sommer, Manfred:
  Alternanten bei gleichmäßiger Approximation mit zweidimensionalen Splinefunktionen.
  In: Böhmer, Klaus ; Meinardus, Günter ; Schempp, Walter (Hrsg.): Spline Functions : proceedings of an international symposium held at Karlsruhe, Germany, May 20 - 23, 1975. - Berlin ; Heidelberg ; New York : Springer, 1976. - S. 339-370. - (Lecture notes in mathematics ; 501)
  ISBN 3-540-07543-7 ; 0-387-07543-7

1975

• 

  Sommer, Manfred:
  Charakterisierung von Minimallösungen in normierten Vektorräumen durch Eigenschaften von Hyperebenen.
  In: Journal of approximation theory. 14 (1975) 2. - S. 103-114.
  ISSN 0021-9045
  (Peer-Review-Journal)