Strictly positive definite functions on a real inner product space

Advances in Computational Mathematics

Volumn 20, Issue 4, 2004, Pages 263-271

  Pinkus, Allan ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Inner product space; Strictly positive definite

Indexed keywords

EID: 4043107083     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1027362918283     Document Type: Article

References (11)

1. C. Berg, J.P.R. Christensen and P. Ressel, Harmonic Analysis on Semigroups (Springer, New York, 1984).
2. C.J.C. Burges and D.J. Crisp, Uniqueness of the SVM solution, in: NIPS (Neural Information Processing Systems), Vol. 12, eds. S.A. Solla, T.K. Leen and K.-R. Müller (2000) pp. 223-229.
3. W. Dahmen and C.A. Micchelli, Some remarks on ridge functions, Approx. Theory Appl. 3 (1987) 139-143.
4. C.H. FitzGerald, C.A. Micchelli and A. Pinkus, Functions that preserve families of positive semidefinite matrices, Linear Algebra Appl. 221 (1995) 83-102.
5. R. Horn and C.R. Johnson, Topics in Matrix Analysis (Cambridge Univ. Press, Cambridge, 1991).
6. G. Pólya and G. Szegö, Problems and Theorems in Analysis, Vol. II (Springer, Berlin, 1976).
7. I.J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942) 96-108.
8. A.J. Smola, B. Schölkopf and K.-R. Müller, The connection between regularization operators and support vector kernels, Neural Networks 11 (1998) 637-649.
9. I. Steinwart, On the influence of the kernel on the consistency of support vector machines, J. Machine Learning Res. 2 (2001) 67-93.
10. I. Steinwart, Support vector machines are universally consistent, Preprint.
11. V.N. Vapnik, The Nature of Statistical Learning Theory (Springer, New York, 1995).