• Nenhum resultado encontrado

Use of the all-Russian mathematical portal Math-Net.Ru implies that you have read and agreed to these terms of use

N/A
N/A
Protected

Academic year: 2024

Share "Use of the all-Russian mathematical portal Math-Net.Ru implies that you have read and agreed to these terms of use"

Copied!
3
0
0

Texto

(1)

Math-Net.Ru

All Russian mathematical portal

S. V. Lyudkovskii, Gaussian measures on free loop spaces, Uspekhi Mat. Nauk, 2001, Volume 56, Issue 5(341), 183–184

DOI: https://doi.org/10.4213/rm444

Use of the all-Russian mathematical portal Math-Net.Ru implies that you have read and agreed to these terms of use

http://www.mathnet.ru/eng/agreement Download details:

IP: 139.59.245.186

November 6, 2022, 23:32:37

(2)

› çÌ

PFJLLBMNHMOF BLFOLF LBGBOM HHCD

SS

È

Μ[ÓÎ

¾

f`]jf dn]jmd]m`Ž`gno‘e^j^ ab

md€nom

glˆˆ^f^ncldab n`

r

h^`p^jfll



dah^Žf dl^]_`

r

j`†

e` a`hlllj^`f^jl^]_`

r

ˆlul_^

dnn dkf dŽ`jde`]mk ’^n de`]jf`^nli_mdull nmdfldn jno‘hd†

q]]`mo‘p^f

n d

ef`]jf dn]jmd‘

Œ (

×Þ

Œ×

]m`Ž`gno‘e^j^ abÖÕ

]֏(א•×gak

pn`h``Žf dul r

l

hg^(×

×

„`jp^^nno^j`_ls

4 B

Ç

dn`nl^]_`^udp_nq j`^e`gpn`€^]jm`m •

R

lal

m •

n dg

R

n duomd^j]k_mdgf dn j`p^] alՕ

{

‹

Õ%‹

>

Ã'

}

hg^%



⊂ N

sâ`hg ddn da`hl n`Š›



udg dij]kl

„]^e df dŽ^ ab no^fl p dn`mo`fl^n jl f`mdnno^

p^jfluq^po^ ]mkuno^ pn`h``Žf dulk ] qhadpl ÆŒÙŒl 

!

”

Œ

”

Œ

”

„_df jodjad]`m

l

 hg^

Ù Õ

Æ

ُƐ

*

⊂ N

efl^peq]jbÝkmak^j]k`Ž…^gl n^nl^p gm q ‘

_dn`nl^]_l‘udp_nq jo‘e`gpn`h``Žf dul r

‰l‰

]qhadpl

‰

‰ • ‰

‰ •Õ‰/

l eLY Ý

Q‰/ • ›Þ  ÝÝ

 (×

‰/Þ ÝÝݐ ‰ l ‰ kmakij]k

×

ŠÃŒ›



×

‰%Œ‰%ã]jk hlmd^po pl m

(

×

hg^

'

∈ {

›ŒË

}

ޏÝà^] al Ž^]_`n^ n`p^fn`j`l p^^j]ke`] a^g`mdj^ ab n`]jbma`€^nno‘

e`gpn`h``Žf dul r

&

Õ

&

∈ N

qg`ma^jm`fki’l‘

 Ý

„

ÝÝÝ



d (

× m

]``jm^j]jm q^j (×

&

•

&

(א

m

&

 Y Ý

Q •  à 1 1ß›

S

ea`jn`

m

 Ù

”

Ù

%

|

,

l p^ij ml gÕ Ù”

Ù

%

‹

Õ

∈ N

 •

$

”

%‹

ŒŒ‹

Œ-

”

%‹

Õ ,  _`hg d •

 d gak aiŽ`r _`pe`n^n jo hf dnl co×mlÆ%

×

6

•

l p^^p`j`Žf d€^nl^ƒ%ÕÆ%

×

efl^p

hg^Օ

{

‹

% Ջ

>

Ã

}

‹•‹

%

∈ R

Õ'

∈ N



s

‚

] al

_`pe d_jn`j`f d]]p`jfl pf duŽl^nlk

]e`p`’bie`gpn`h``Žf dul r

]qhadpl

0

_`f dup^fn`]jl›mjd_l^j`•

S

%

%hg^%„e`gpn`h``Žf dulk%

0



”

%

0

*

6

• ' UÝQWPf%YÝRQ% • Ã

⊂ N

s ¾q]jb *ŒÞ

„ ef`]jf dn]jmd n^ef^fom no‘ _q]` n` ]`Ž` a^m]_l‘

*

ã

ˆqn_cl r

Š›



] n`fp`

r

*

 Օ

ˆP

”

k

|

,

k

,

˜

efl

*ŒÞl*•ß

mef`jlm n`p] aqd^

hg^

, )

>

-

∈ N

 -

>

ŠÀ

ˍ

ߛ • Y Ý

Q s

¾

q]jb *

Œ



„

‡

j` e`e` an^nl^

W [

V

ã Ý

M Y%

*

Œ

Þ

%e`n`fp^

k

k 0

* ՕÝMd*dgak`hf dnl^nn`

r

`Žad]jl m

R

]

_q]` n`

ã hf dnl c^

r

eq]jb !

 Œ



„

e`gef`]jf dn]jm`j^‘Ö

 Œgak_`j`fo‘

k

Ö

k

! Օ

`P

%

×



k

Ö

k

%À'"

´

1

hg^

k

Ö

k

% Օ 

k

Ö

k 0

%



k

Ö

k 0

%



efl'

>

›l

k

Ö

k

× •

k

Ö

k 0

×Ã1“ 1

s‚] al „‡j``hf dnl^nn dk`Žad]jbm

]_q]` n`

ã hf dnl c^

r



d

„e`gef`]jf dn]jmd

&lYÝQ •

∈ N

eU

`S

´

•

j`

udg dgl p

!

!

 ŒÕ•W [

V

ã Ý

M Y !

 Œhg^ •

d

 Œ`ef^g^ al p

e`e` an^nl^p

!

!

 Œ

e`n`fp^

k

Ö

k

Օ

ˆP

k

Ö

|

#$

k

%&'

#$

À"

& (

˜

hg^

Ã1Ü1

l) • *Œ“ŒÜs¾q]jb l kmakij]k!

0

(

0

ã

pn`h``Žf dulk pl ]Ã1“

0

1“l

Ã1Ü

0

1Üs#e`p`’bidjad]`ml

`ef^g^ al pef`]jf dn]jmd

Œ

l

Œ(×

Þ

Œ×

hg^

)

•



*

Œ“ŒÜ

s

‚

] al _`pe d_jn`

l

Ö

Œ

 l p^^j

f dnh

VRMTÖ‹

• Y Ý

Q

‹

 j` ֏ kmak^j]k

ã

e`gpn`h``Žf dul^p m

l n d ֏ udg dgl p

]mkun`]jb 0

^ml

ã Å

lmljdl

fl p dn`m

‡

a^p^n j`Ž…^p d jd_`

r



j`Ö

• › s

Á

j` l ngqcl fq^j a`_dab no^ n`fp dab no^ _``fgl n djo m ֏

s \

] aqd^ •

e` aql pe df dp^jf]``jm^j]jm q i’l r

gal n^

gqhln d _flm`

rs‚

] algakÖ

Œ

l p^^j]k

e`] a^g`mdj^ ab n`]jbÖ

|

$

Œ

]‘`gk ’ dk]k_Öj`e` aql p +



»

Œ



l "

+

ÖŒ

 ] "

+

+ • Ö hg^ » „ ‡j` _mdgf dn j m

R

lal

s \

]laq  Ý

„

Ýà



l p^^j]kma`€^nl^)

Õ



Œ

Œ

Š›



Š ˍs

\

]`^jdnll]moŽ`f`pn djqf dab no‘

_``fgl n dj e` aqd^p n^ef^fom nq i _`pe`ul cli Ø

Ö m Օ

Œ(×Þ

Œ× jd_q i j`

(3)

›

Ø

× • Ø hg^ ׏ •

{

×

}

s\`ub p^p ea`jnor e`ghfqee`l g

0

Օ

0

Œ(×Þ

0

Œ× ]

)

0

• *Œ“

00

Ά

00

hg^à 1Û

0

1“

0

1“

00

1“ 1

l à 1"

00

1Ü

0

1Ü

00

1Ü 1



0

„ ‡j`

!

0

00

ã

e`gpn`h``Žf dul^ea`jn`^m

s

A T

ZœZžW S

°¨§zªªw«

y

|¡z|¡¢©z|¢¥©°~««­©°§«°­¢­°² |¡¥w­|¬­w y

«¯¯|§|­

x

¦«§z|v°²v|§

°

w¢­w¡«¢|{£­w

ªw y

¨§zªªw«

y

°

0

¸

–

akg`_dudj^ ab]jmdf d]]p`jfl p

κ ∈

0

Œ

jd_j`

κ

ÕgM[

\



\

‰/



„

h`p^`p`fˆluphg^

„

e`gpn`h``Žf dul^]qhadpl_`f dup^fn`]jl

›m



„

_mdgf dn j

m s

–

ak ]q’^]jm q^j `j`Žf d€^nl^

Œ

Ú Օ

Z

×

· · · Z

$

×





à 1“

6

“

00

1



hg^

»

•

L

%

×

%



%

„ef`]jf dn]jm`glˆˆ^f^ncldab no‘'

ã

ˆ`fp n d

Ú •

κ



• ŠÃŒ›





.

•

× · · · ×

. ]% •

' • ›ŒŒ(efl^p (

>

Y

Ý

QÀY Ý

Q

s

–

ake`] a^g`mdj^ ab n`]jlhlabŽ^f j`mo‘ef`]jf dn]jm

!

n dg

R

]

⊂ N

eq]jb



{

!

Õ

}

 Օ

{

‹ • ‹ Ջ

!

Œ

Þ

k

‹

k

{

}

Օ

`P

k

‹

k

´

1

∞}

hg^

,

>

Ãs

\

`ub p^p

!

•



»



× R

hg^•

N

eflYÝQ

•

•

{

›

}

efl

Y Ý

Q

1

s¾q]jb



{

!

Õ

}



jd_l^j`

Õ

!



{

!

Õ

}

„

ma`€^nlk]



!

l

k

k

{

}

•› s

‚

] al

Y Ý

Q

•

j`udg dgl p`j`Žf d€^nl^

Œ Õ•

{



|

$Œ

|

$Õ

∈ N }

hg^

`ef^g^ a^nogak

e

•

eflY

Ý

Q

•

l

e

„e`gpn`h``Žf dul^m

Օ

N

%

%



p`g^ al fq^p`^

n d

0



{

% Õ '

∈ N }

 ] % •

' hg^ Ã 1 )

“ 1 “

“

00

ÀË l

Ã1

Ü1Ü

Ü

00

ÀËj`e` aql p`j`Žf d€^nl^ Œ Õ•

P





|

$Œ

|

$

hg^

Õ

Œ

»



Œ

»

 „ ma`€^nlks ¾q]jb • 

∈ R

Õ

∈ N

 hg^

•



|

$Œ

|

$

|

κ

 " • Y Ý

Q

»

.

$



•



%

Õ ' • ›ŒŒ"

s â

`hg d

k

k

Օ

P



k

k

À"

&

 1

 hg^

k

k

Օ

P

%

|

%

|

Þ hlabŽ^f j`m` ef`]jf dn]jm` jd_l‘e`] a^g`mdj^ ab n`]j^

r

`Ž`un dl p

s â

`hg d

l

‡

_]e`n^ncldab n`^ `j`Žf d€^nl^

%

pn`h``Žf dulk



Œ

 e`f`€g dij `j`Žf d€^nl^

Õ

×

!

!

0

× hg^ !

0

× „ `_f^]jn`]jb nqak m hlabŽ^f j`m`p ef`]jf dn]jm^

Օ

!

Œ

(

×Þ

»

Œ(×

×

Ð

×

s

¾

q]jb

ÖŒ  Օ



 Ý

Y



ÖŒ

h i

 hg^ ÖŒ  Օ ÖŒ  • Ëefl YÝQ , ›l • Ìefl YÝQ • ›s

\

`ub p^p

!

•

∈ N

s #q’^]jm q^j ]^p^r]jm`

{

”

Õ* • ›ŒŒ"Þ

∈ N

Þ

∈ N } ⊂

!

0

00

*

00

Œ(×

Þ

»

e 0

Œ×

×

Ð gak “

0

12

00

1“

00

 Ü

0

1-

00

1Ü

00

jd_`^

j` `j`Žf d€^nl^ Ö Օ

P

P

∈ N

P

”

ÖŒ ”



l n…^_jlm n` hg^

»

e 0

„

‡

j`

!

0

00

ã

e`gpn`h``Žf dul^

m

L

%

×

%

e

0

 ”

n^udml]l po `j a`_dab no‘ _``fgl n dj

‹

&

Œ‹

&

Œ

* ls¾`‡j`pq „glˆˆ^`p`fˆlup`_f^]jn`]jl Æ×

3

×

Œ(×Þ

Œ×n d`_f^]jn`]jb

!

×

3

ÃmhlabŽ^f j`m`pe`gef`]jf dn]jm^

× m



{

!

Õ

}

s

#

q’^]jm q ij `_f^]jn`]jl

!

0 3

×

0

l Æ

3

×

jd_l^j` !

0

Æ

Æ×s¾q]jb

ÚÕ•

Ú

Ú]Ú

!

!

0

hg^!•Æ s¾`‡j`pqhdq]]`mdp^f dn d×]

e`p`’bil ngqcl fq^jp^fq

n d

]p s

jd_€^

Š›





Š ˍ

 s

á

#šÇ0

á

â‚ä1â2 ä3

Š 4

66

#> ??

–

`_a s

ä1

™ sË

ÃÃÃ sâsÌ

à såÌs#s

Ì

Ã/„

Ì

à çs

Š A6^6

F c

E c

s

OMOVRU Ý

OY X

L L f

VLP f

WL d

!LQ f

UOjRM Ýd

LU YW s

ZVO f

V Ý

M [

Q R [ks

S?

ææ

›Ãà ç

/ sX

LW!U RQLWÕ X

LW

!U RQLWNR [sX

R s

› æææs

án]jljq j`Ž’^

r

ˆlul_l ä1

™

¾

fl nkj`f^g_` aa^hl^

r

ËËs çsË

Referências

Documentos relacionados