000 02527nam a22003738i 4500
001 CR9780511526244
003 UkCbUP
005 20200124160239.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090407s1995||||enk o ||1 0|eng|d
020 _a9780511526244 (ebook)
020 _z9780521470148 (hardback)
020 _z9780521059831 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA274.75
_b.P56 1995
082 0 0 _a519.2/33
_220
100 1 _aPinsky, Ross, G.,
_eauthor.
245 1 0 _aPositive harmonic functions and diffusion /
_cRoss G. Pinsky.
246 3 _aPositive Harmonic Functions & Diffusion
264 1 _aCambridge :
_bCambridge University Press,
_c1995.
300 _a1 online resource (xvi, 474 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v45
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aIn this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
650 0 _aDiffusion processes.
650 0 _aElliptic operators.
776 0 8 _iPrint version:
_z9780521470148
830 0 _aCambridge studies in advanced mathematics ;
_v45.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511526244
999 _c518405
_d518403