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anisotropic magnetic fields, weakly conjugate operator, absolutely continuous spectrum 
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%%Page: 3 3
bop 83 482 a Fy(elemen)m(t)32 b(of)e Fl(B)5 b Fv(\()p Fk(G)688
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Fl(;)15 b Fv(I)-18 b(R)515 968 y Fi(n)562 1004 y Fv(\))32 b
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b(magnetic)h(momen)m(tum,)i(whic)m(h)e(is)e(the)h(closure)g(of)f
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y Fi(j)2222 1520 y Fv(+)20 b Fl(V)g Fv(\()p Fl(Q)p Fv(\))83
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3746 y Fj(21)2058 3732 y Fy(will)31 b(b)s(e)g(written)h(simply)e
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3771 y Fh(\000)399 3845 y Fl(D)477 3812 y Fi(Y)537 3845 y Fl(h)589
3771 y Fh(\001)647 3845 y Fv(\()p Fl(y)s(;)15 b(z)t Fv(\))26
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y Fi(j)2052 3845 y Fl(h)p Fv(\)\()p Fl(y)s(;)15 b(z)t Fv(\))p
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4387 y(\(i\))309 4309 y Fh(\014)309 4364 y(\014)339 4387 y
Fl(B)413 4354 y Fi(Y)474 4387 y Fv(\()p Fl(y)s Fv(\))592 4309
y Fh(\014)592 4364 y(\014)648 4387 y Fk(\024)879 4351 y Fi(c)p
754 4366 282 4 v 754 4420 a Fj(1+)p Fb(j)p Fi(y)r Fb(j)921
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4708 y Fh(\020)1998 4809 y Fv(2)20 b Fk(\000)2167 4773 y Fj(1)p
2164 4788 41 4 v 2164 4840 a Fi(\015)2215 4708 y Fh(\021)2294
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5188 y Fl(G)496 5202 y Fb(\006)555 5188 y Fv(\()p Fl(y)s(;)15
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b Fk(\000)1118 5126 y Fv(1)p 1115 5167 53 4 v 1115 5250 a Fl(\015)1197
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5188 y Fk(\006)p Fl(B)1595 5150 y Fi(Y)1655 5188 y Fv(\()p
Fl(y)s Fv(\))1773 5114 y Fh(\003)1832 5188 y Fk(\000)1923 5114
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5836 y Fy(3)p eop
%%Page: 4 4
bop 121 482 a Fd(\(iv\))45 b(Ther)-5 b(e)33 b(ar)-5 b(e)34
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Fj(1)1522 482 y Fl(;)15 b(c)1601 496 y Fj(2)1641 482 y Fl(;)g(c)1720
496 y Fj(3)1793 482 y Fd(such)33 b(that)357 592 y Fh(\014)357
647 y(\014)387 669 y Fl(D)465 632 y Fi(Y)541 596 y Fh(\000)583
669 y Fl(D)661 632 y Fi(Y)721 669 y Fl(V)795 596 y Fh(\001)851
669 y Fv(\()p Fl(y)s(;)15 b(z)t Fv(\))1055 592 y Fh(\014)1055
647 y(\014)1107 669 y Fv(+)20 b Fk(j)p Fl(y)s Fk(j)1296 632
y Fj(2)1351 596 y Fh(\000)1393 669 y Fl(D)1471 632 y Fi(Y)1531
669 y Fl(B)1605 632 y Fi(Y)1665 596 y Fh(\001)1707 613 y Fj(2)1762
669 y Fv(\()p Fl(y)s Fv(\))25 b Fk(\024)g Fl(c)2040 683 y Fj(1)2095
596 y Fh(\002)2133 669 y Fk(\006)p Fl(B)2278 632 y Fi(Y)2338
669 y Fv(\()p Fl(y)s Fv(\))2456 596 y Fh(\003)2515 669 y Fv(+)20
b Fl(c)2645 683 y Fj(2)2684 669 y Fl(G)p Fv(\()p Fl(y)s(;)15
b(z)t Fv(\))21 b(+)f Fl(c)3111 683 y Fj(3)3151 669 y Fk(j)p
Fl(y)s Fk(j)3249 632 y Fj(2)3304 596 y Fh(\000)3346 669 y Fl(B)3420
632 y Fi(Y)3480 596 y Fh(\001)3522 613 y Fj(2)3576 669 y Fv(\()p
Fl(y)s Fv(\))p Fl(:)83 899 y Fd(Then:)144 1129 y(\(a\))45 b
Fk(k)p Fv(\()p Fl(H)28 b Fk(\000)20 b Fl(\025)g Fk(\007)g Fl(i\027)6
b Fv(\))865 1096 y Fb(\000)p Fj(1)960 1129 y Fk(k)1005 1148
y Fi(B)s Fj(\()p Fb(A)p Fi(;)p Fb(A)1220 1129 y Fa(\003)1258
1148 y Fj(\))1314 1129 y Fk(\024)25 b Fl(c)p Fd(,)33 b(uniformly)e(in)h
Fl(\025)25 b Fk(2)g Fv(I)-18 b(R)o Fl(;)48 b(\027)31 b(>)25
b Fv(0)p Fd(.)149 1306 y(\(b\))45 b(A)n(l)5 b(l)32 b(the)h(elements)g(of)f
Fl(B)5 b Fv(\()p Fk(A)1266 1273 y Fb(\003)1305 1306 y Fl(;)15
b Fk(H)q Fv(\))32 b Fd(ar)-5 b(e)34 b(\(glob)-5 b(al)5 b(ly\))33
b Fl(H)7 b Fd(-smo)-5 b(oth)33 b(op)-5 b(er)g(ators.)149 1482
y(\(c\))45 b Fl(H)39 b Fd(has)33 b(only)f(pur)-5 b(ely)33 b(absolutely)h(c)-5
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b(2.3)45 b Fy(In)32 b(their)h(greatest)h(generalit)m(y)-8 b(,)35
b(the)e(spaces)f Fk(A)g Fy(and)h Fk(A)2563 1698 y Fb(\003)2634
1731 y Fy(whic)m(h)h(app)s(ear)f(in)g(the)g(limiting)83 1844
y(absorption)f(principle)g(will)f(b)s(e)f(constructed)j(in)d(Section)i(4.)42
b(But)31 b(under)g(one)g(not)g(to)s(o)g(restrictiv)m(e)h(extra)83
1957 y(condition,)39 b(w)m(e)e(can)g(giv)m(e)f(a)h(v)m(ery)f(transparen)m(t)i
(v)m(ersion.)58 b(Assume)36 b(that)h Fl(B)2767 1924 y Fi(Y)2827
1957 y Fv(\()p Fl(y)s Fv(\))f Fl(>)e Fv(0)j Fy(for)f(all)g
Fl(y)i Fk(2)d Fv(I)-18 b(R)3704 1921 y Fj(2)3743 1957 y Fy(.)83
2070 y(Then)29 b(w)m(e)g(can)f(de\034ne)h Fl(F)13 b Fv(\()p
Fl(y)s Fv(\))26 b(=)f(max)1365 1996 y Fh(\010)1418 2070 y Fl(B)1492
2037 y Fi(Y)1553 2070 y Fv(\()p Fl(y)s Fv(\))1671 2037 y Fb(\000)p
Fj(1)p Fi(=)p Fj(2)1836 2070 y Fl(;)15 b Fk(j)p Fl(y)s Fk(j)1974
1996 y Fh(\011)2056 2070 y Fy(and)28 b(set)g Fk(F)38 b Fy(the)28
b(completion)i(of)e Fk(D)i Fy(with)f(resp)s(ect)83 2183 y(to)37
b(the)g(norm)g Fk(k)p Fl(f)10 b Fk(k)749 2197 y Fb(F)846 2183
y Fv(=)36 b Fk(k)p Fl(F)13 b Fv(\()p Fl(Q)p Fv(\))p Fl(f)d
Fk(k)p Fy(.)60 b(In)36 b(the)h(p)s(oin)m(ts)g Fv(\()p Fl(a)p
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%%Page: 7 7
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%%Page: 10 10
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Fv(=)42 b Fk(f)p Fv(0)p Fk(g)p Fl(;)15 b(B)49 b Fv(=)42 b(0)f
Fy(and)g Fl(V)63 b Fv(=)42 b(0)p Fy(,)i(w)m(e)d(get)g(a)g(result)g(whic)m(h)h
(w)m(as)f(not)g(kno)m(wn)83 4142 y(for)34 b(quite)h(a)f(long)h(time.)54
b(W)-8 b(e)34 b(send)h(to)f([Si,2)q(])g(and)h([KY])g(where,)h(ho)m(w)m(ev)m
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b(are)f(presen)m(ted.)42 b(In)28 b([MP)q(])g(the)h(metho)s(d)g(of)f(the)h(w)m
(eakly)g(conjugate)h(op)s(erator)f(is)f(used)h(to)g(deduce)83
4368 y(global)j(smo)s(oth)e(op)s(erators)i(for)e(op)s(erators)h(of)g(m)m
(ultiplication)i(b)m(y)e(a)g(rather)g(large)h(class)e(of)h(functions)g(in)83
4480 y(a)f(uni\034ed)i(manner.)83 4838 y Fm(References)83 5078
y Fy([AHS])108 b(A)-10 b(vron)27 b(J.,)i(Herbst)e(I.,)h(Simon)g(B.:)39
b(Sc)m(hr\366)s(dinger)30 b(op)s(erators)e(with)g(magnetic)h(\034elds,)f(I.)f
(General)427 5191 y(in)m(teractions.)32 b(Duk)m(e)f(Math.)g(J.)f
Fw(45)p Fy(,)g(847-883)i(\(1978\).)83 5379 y([BKM])77 b(Boutet)42
b(de)f(Mon)m(v)m(el)h(A.,)h(Kazan)m(tsev)-5 b(a)42 b(G.,)i(M)p
Fv(\025)-45 b Fy(an)m(toiu)42 b(M.:)61 b(Some)42 b(anisotropic)g(Sc)m(hr\366)
s(dinger)427 5491 y(op)s(erators)31 b(without)g(singular)g(sp)s(ectrum.)g
(Helv.)f(Ph)m(ys.)h(A)m(cta,)g(V)-8 b(ol.)31 b Fw(69)p Fy(,)f(13-25)h
(\(1996\).)1880 5836 y(10)p eop
%%Page: 11 11
bop 83 482 a Fy([BM])147 b(Boutet)37 b(de)g(Mon)m(v)m(el)g(A.,)h(M)p
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(ysics,)h(V)-8 b(ol.)31 b Fw(488)p Fy(.)83 782 y([BP])169 b(Boutet)24
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b(Cycon)37 b(H.L.,)h(F)-8 b(ro)s(ese)37 b(R.G.,)h(Kirsc)m(h)f(W.,)h(Simon)f
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b(with)f(Appli-)427 1196 y(c)-5 b(ation)45 b(to)f(Quantum)h(Me)-5
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b(\(1987\).)83 1496 y([Ka])179 b(Kato)24 b(T.:)37 b(Notes)24
b(on)g(some)f(inequalities)i(for)e(linear)i(op)s(erators.)f(Math.)g(Annalen)g
Fw(125)p Fy(,)h(208-212)427 1609 y(\(1952\).)83 1797 y([KY])156
b(Kato)27 b(T.,)h(Y)-8 b(a)5 b(jima)28 b(K.:)39 b(Some)27 b(examples)g(of)g
(smo)s(oth)g(op)s(erators)g(and)g(the)h(asso)s(ciated)f(smo)s(oth-)427
1910 y(ing)k(e\033ect.)f(Rev.)g(Math.)h(Ph)m(ys.)f Fw(1)p Fy(,)h(481-496)g
(\(1989\).)83 2097 y([MP])150 b(M)p Fv(\025)-45 b Fy(an)m(toiu)40
b(M.,)h(P)m(ascu)g(M.:)57 b(Global)40 b(resolv)m(en)m(t)g(estimates)g(for)f
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b(Th.)g Fw(36)p Fy(,)f(283-294)h(\(1996\).)83 2398 y([MS])161
b(Miller)23 b(K.,)h(Simon)g(B.:)37 b(Quan)m(tum)24 b(magnetic)g(Hamiltonians)
g(with)f(remark)-5 b(able)24 b(sp)s(ectral)f(prop-)427 2511
y(erties.)31 b(Ph)m(ys.)f(Rev.)g(Lett.)h Fw(44)p Fy(,)f(1706-1707)i
(\(1980\).)83 2698 y([RS])177 b(Reed)22 b(M.,)i(Simon)f(B.:)36
b Fd(Metho)-5 b(ds)26 b(of)f(Mo)-5 b(dern)26 b(Mathematic)-5
b(al)25 b(Physics,)h(V)-7 b(olume)26 b(IV)p Fy(.)c(New)h(Y)-8
b(ork:)427 2811 y(A)m(cademic)32 b(Press)e(\(1975\).)83 2999
y([Si,1])149 b(Simon)29 b(B.:)39 b(The)29 b(b)s(ound)f(states)g(of)f(w)m
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(w)m(o)427 3112 y(dimensions.)j(Annals)f(of)g(Ph)m(ysics)h
Fw(97)p Fy(,)f(279-288)i(\(1976\).)83 3299 y([Si,2])149 b(Simon)40
b(B.:)58 b(Best)39 b(constan)m(ts)i(in)e(some)h(op)s(erator)g(smo)s(othness)f
(estimates.)h(J.)f(F)-8 b(unct.)41 b(Anal.)427 3412 y Fw(107)p
Fy(,)30 b(66-71)h(\(1992\).)83 3600 y([W)-8 b(e])169 b(W)-8
b(eidl)25 b(T.:)38 b(A)23 b(remark)i(on)g(Hardy)f(t)m(yp)s(e)g(inequalities)h
(for)f(critical)h(Sc)m(hr\366)s(dinger)i(op)s(erators)d(with)427
3713 y(magnetic)32 b(\034elds.)e(Preprin)m(t)j(and)d(to)h(app)s(ear)g(in)f
(Pro)s(ceedings)i(F)-10 b(A98.)83 3900 y([Y)i(a])189 b(Y)-8
b(amada)37 b(O.:)51 b(Sp)s(ectral)37 b(theory)f(of)f(magnetic)i(Sc)m(hr\366)s
(dinger)g(op)s(erators)g(with)f(explo)s(ding)g(p)s(o-)427 4013
y(ten)m(tials.)31 b(J.)g(Math.)g(Ky)m(oto)g(Univ.)f Fw(30-4)p
Fy(,)g(585-623)h(\(1990\).)1880 5836 y(11)p eop
%%Trailer
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userdict /end-hook known{end-hook}if
%%EOF
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