Content-Type: multipart/mixed; boundary="-------------0106250633603" This is a multi-part message in MIME format. ---------------0106250633603 Content-Type: text/plain; name="01-227.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="01-227.keywords" lower bounds, quantum dynamics, multifractal dimensions ---------------0106250633603 Content-Type: application/postscript; name="lb.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="lb.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: lb.dvi %%Pages: 28 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: C:\DVIPS\BIN\WIN32\DVIPS.EXE lb.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2001.06.25:1304 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N 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b(\014rst)f(statemen)m(t)j(is)d(pro)m(v)m(en)h(in)f([4)q (].)39 b(The)26 b(pro)s(of)f(for)h Fl(q)i(>)d Fm(1)h(is)f(trivial)f (and)i(w)m(ell)f(kno)m(wn.)38 b(It)27 b(w)m(as)0 5331 y(conjectured)d(man)m(y)g(y)m(ears)h(ago)g(that)g(the)f(result)f (should)f(also)i(hold)e(for)i Fl(q)k Fk(2)d Fm(\(0)p Fl(;)15 b Fm(1\).)40 b(Ho)m(w)m(ev)m(er,)28 b(unlik)m(e)22 b(it)i(w)m(as)0 5444 y(stated)31 b(in)f(man)m(y)g(phisicist's)e(pap)s (ers,)i(the)h(pro)s(of)f(for)g Fl(q)e Fk(2)e Fm(\(0)p Fl(;)15 b Fm(1\))32 b(is)e(not)g(the)h(same)g(and)f(rather)h(non)m (trivial.)0 5557 y(Only)e(in)g([4)q(])h(it)g(w)m(as)h(rigorously)d(pro) m(v)m(en)j(in)e(all)g(generalit)m(y)i(\(for)f(an)m(y)h(Borel)g (probabilit)m(y)c(measure\).)1845 5806 y(15)p eop %%Page: 16 16 16 15 bop 141 390 a Fm(The)30 b(third)f(statemen)m(t)j(follo)m(ws)d (from)h(the)h(second)f(if)f(one)i(tak)m(es)h Fl(R)q Fm(\()p Fl(u)p Fm(\))26 b(=)f(\()p Fk(j)p Fl(u)p Fk(j)2875 357 y Fh(2)2935 390 y Fm(+)20 b(1\))3106 357 y Ff(\000)p Fh(1)3201 390 y 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2607 y(of)30 b(op)s(erators,)h(Academic)g(Press,)f(1978.)0 2795 y([23])581 b(B.)38 b(Simon,)h Fl(L)1223 2762 y Fj(p)1262 2795 y Fm(-norms)e(of)h(the)g(Borel)g(transform)f(and)h(the)g(decomp)s (osition)e(of)i(mea-)721 2907 y(sures,)30 b(Pro)s(c.)g(Amer.)h(Math.)g (So)s(c.)f Fn(123)h Fm(\(1995\),)j(3749-3755.)0 3095 y([24])581 b(S.)53 b(Tc)m(heremc)m(han)m(tsev,)60 b(Ho)m(w)54 b(to)f(pro)m(v)m(e)h(dynamical)d(lo)s(calization,)58 b(to)c(app)s(ear)e(in)721 3208 y(Comm.)30 b(Math.)h(Ph)m(ys.,)g(mp)p 1716 3208 28 4 v 32 w(arc)g(00-443.)0 3396 y([25])581 b(S.)30 b(Tc)m(heremc)m(han)m(tsev,)i(in)d(preparation.)1845 5806 y(28)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0106250633603--