By Elias M. Stein
This ebook has as its topic the boundary price conception of holomorphic services in different advanced variables, a subject that's simply now coming to the vanguard of mathematical research. For one variable, the subject is classical and very well understood. in numerous variables, the mandatory realizing of holomorphic services through partial differential equations has a contemporary starting place, and Professor Stein's ebook, which emphasizes the potential-theoretic elements of the boundary price challenge, may still turn into the normal paintings within the field.
Originally released in 1972.
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Extra info for Boundary behavior of holomorphic functions of several complex variables
73) An interesting gc~ncralizationof thc hlittag-Lemer fi111ctio11to scvcr;il variables has been suggested by S. B. I-Iadid rid Yu. Lucllko ,who used it for solving lincvtr fractiorlal difi'crciitial ecluatiolis with constant coc#icicnts 1)y the operatiollal rr~etliotl: n lrl ( k :11. . , LTrL) C 1, 2) /=I . + l,,, = k . . I,, > 0 whcrc (k: 1 1 , . . 2 arc multii~orriialcocfficicnts [ 2 ] . 57), the Alittag-Lefflcr functiori E,,,,-l(z) is a gc11er;tlization of thc expo~icritialfunction ez a ~ i d ,tlicrcfore.
Was in fact i n t r o d u c ~ dby Agarwal [:$I. A iiurnbcr of rclatiorisliips for tliis filnctiori were ohtaincd by I-Iurnbert and Agarwal [I071 usirig the Laplact. transforni tcchriique. This fiiriction could have been c~allrdthr Agarwsl function. However, Hurribert sritl Agarwal generously left the same notation as for the oneparanieter blittag-lcffler function, and that is the reason that 11ow the two-parameter fu~ictionis called thc RIittng-Lcfflcr filnctioii. M;e will use the. narnc. a ~ i dthe notation uscd in the fi~ritlarnc~rital haritft>ook on spcxcinl functions .
Olc: in tile theory of integer-ordvr. 2. AIITTAG-LEFFLER FUNCTION 17 was ir~troducedby G. 11. hlittag-Lcfflcr [155, 156, 1571 arid studied also by A. Wiriiari [256. 2571. Thr>two-~)ararnc~tcr function of thc Mittag-Lcfflcr type, which plays a vcry irriportant role in the fractior~alcalculus. was in fact i n t r o d u c ~ dby Agarwal [:$I. A iiurnbcr of rclatiorisliips for tliis filnctiori were ohtaincd by I-Iurnbert and Agarwal [I071 usirig the Laplact. transforni tcchriique. This fiiriction could have been c~allrdthr Agarwsl function.