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Volumn 36, Issue 3, 2012, Pages 399-441

Left-inverses of fractional Laplacian and sparse stochastic processes

Author keywords

Fractional Laplacian; Fractional stochastic process; Impulsive Poisson noise; Riesz potential; Stochastic partial differential operator

Indexed keywords


EID: 84858280734     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-011-9183-6     Document Type: Article
Times cited : (17)

References (14)
  • 1
    • 34147186355 scopus 로고    scopus 로고
    • Self-similarity Part II: optimal estimation of fractal processes
    • Blu, T., Unser, M.: Self-similarity Part II: optimal estimation of fractal processes. IEEE Trans. Signal Process. 55, 1364-1378 (2007).
    • (2007) IEEE Trans. Signal Process. , vol.55 , pp. 1364-1378
    • Blu, T.1    Unser, M.2
  • 2
    • 37849049246 scopus 로고    scopus 로고
    • Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
    • Caffarelli, L. A., Salsa, S., Silvestre, L.: Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian. Invent. Math. 171, 425-461 (2008).
    • (2008) Invent. Math. , vol.171 , pp. 425-461
    • Caffarelli, L.A.1    Salsa, S.2    Silvestre, L.3
  • 3
    • 77955474529 scopus 로고    scopus 로고
    • Heat kernel estimates for Dirichlet fractional Laplacian
    • Chen, Z.-Q., Kim, P., Song, R.: Heat kernel estimates for Dirichlet fractional Laplacian. J. Eur. Math. Soc. 12, 1307-1329 (2010).
    • (2010) J. Eur. Math. Soc. , vol.12 , pp. 1307-1329
    • Chen, Z.-Q.1    Kim, P.2    Song, R.3
  • 4
    • 0001935440 scopus 로고
    • Splines minimizing rotation-invariant semi-norms in Sobolev spaces
    • In: eds. Schempp, W., Zeller, K. Springer
    • Duchon, J.: Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: eds. Schempp, W., Zeller, K.: Constructive Theory of Functions of Several Variables, pp. 85-100. Springer (1977).
    • (1977) Constructive Theory of Functions of Several Variables , pp. 85-100
    • Duchon, J.1
  • 5
    • 33644513654 scopus 로고    scopus 로고
    • A Modern Approach to Probability Theory
    • Fristedt, B., Gray, L.: A Modern Approach to Probability Theory. Birkhauser (1997).
    • (1997) Birkhauser
    • Fristedt, B.1    Gray, L.2
  • 8
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • Mandelbrot, B. B., van Ness, J. W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422-437 (1968).
    • (1968) SIAM Rev. , vol.10 , pp. 422-437
    • Mandelbrot, B.B.1    van Ness, J.W.2
  • 9
    • 34250592431 scopus 로고
    • L'intégrale de Riemann-Liouville et le probléme de Cauchy
    • Riesz, M.: L'intégrale de Riemann-Liouville et le probléme de Cauchy. Acta Math. 81, 1-223 (1949).
    • (1949) Acta Math. , vol.81 , pp. 1-223
    • Riesz, M.1
  • 10
    • 33747032243 scopus 로고    scopus 로고
    • Hölder estimates for solutions of integro-differential equations like the fractional Laplace
    • Silvestre, L.: Hölder estimates for solutions of integro-differential equations like the fractional Laplace. Indiana Univ. Math. J. 55, 1155-1174 (2006).
    • (2006) Indiana Univ. Math. J. , vol.55 , pp. 1155-1174
    • Silvestre, L.1
  • 12
    • 63449140122 scopus 로고    scopus 로고
    • Invariances, Laplacian-like wavelet bases, and the whitening of fractal processes
    • Tafti, P. D., van De Ville, D., Unser, M.: Invariances, Laplacian-like wavelet bases, and the whitening of fractal processes. IEEE Trans. Image Process. 18, 689-702 (2009).
    • (2009) IEEE Trans. Image Process. , vol.18 , pp. 689-702
    • Tafti, P.D.1    van de Ville, D.2    Unser, M.3
  • 14
    • 79951629005 scopus 로고    scopus 로고
    • Stochastic models for sparse and piecewise-smooth signals
    • Unser, M., Tafti, P. D.: Stochastic models for sparse and piecewise-smooth signals. IEEE Trans. Signal Process. 59, 989-1006 (2011).
    • (2011) IEEE Trans. Signal Process. , vol.59 , pp. 989-1006
    • Unser, M.1    Tafti, P.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.