Differential operators on Hermite Sobolev spaces View Full Text


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Article Info

DATE

2015-02

AUTHORS

SUPRIO BHAR, B RAJEEV

ABSTRACT

In this paper, we compute the Hilbert space adjoint ∂∗ of the derivative operator ∂ on the Hermite Sobolev spaces Sq. We use this calculation to give a different proof of the ‘monotonicity inequality’ for a class of differential operators (L,A) for which the inequality was proved in Infin. Dimens. Anal. Quantum Probab. Relat. Top.2(4) (2009) 515–591. We also prove the monotonicity inequality for (L,A), when these correspond to the Ornstein–Uhlenbeck diffusion. More... »

PAGES

113-125

References to SciGraph publications

  • 2008-03. Probabilistic Representations of Solutions of the Forward Equations in POTENTIAL ANALYSIS
  • 2014. Stochastic Differential Equations in Infinite Dimensions in COMPUTER VISION
  • 1981-07. Stochastic evolution equations in JOURNAL OF SOVIET MATHEMATICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s12044-015-0220-0

    DOI

    http://dx.doi.org/10.1007/s12044-015-0220-0

    DIMENSIONS

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