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Equations fonctionnelles pour une fonction sur<br />un espace singulier

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(1)Equations fonctionnelles pour une fonction surun espace singulier Tristan Torrelli. To cite this version: Tristan Torrelli. Equations fonctionnelles pour une fonction surun espace singulier. Mathématiques [math]. Université Nice Sophia Antipolis, 1998. Français. �tel-00011262�. HAL Id: tel-00011262 https://tel.archives-ouvertes.fr/tel-00011262 Submitted on 23 Dec 2005. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(11) [Ïf dl×1_cb\o\mK_ q Ø p _ n m Ü b\_"o g qcf ¿ Z\n _+Ù@_ o\_ ` ` f Ø nKg dlm f b\`,o\_—E | dl× _ ] fh[c_cÐ ¿"_‚ÀkÅ Å ÅGÀ$‰+Åsu_+dada_ Ü*_ ] b _ ] [ } n mK`l}Údam f b-} Z\Z } [ 2} ˜Gd¿J}kmÇbeda_cb€}kbed Ø,` g m ¾ }Úbd n _ Z5f mÇbed'o\_ ¾^g _o\_ÛNÅ3‚_ j × fhg dØ qcf ¿"¿J_ g b q }k`Ed [c_ Ð ` Z } [ dam q g\n mK_ [ o g da× _ ] fh[c_cÐ ¿"_o1_ys f ¿ Z } [ }kmK` f bo\8_

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(13) d @ ‹e`am Ü b€} nKf b\`#} g"Z }k`Ï`l} Ü _ n } Z1[ _ g@¾ _o\_ÛNÅ5_ j × fkg d Z } [i[^_ ] qcg\[Ï[ _cb q _'` g\[ n }Eo\mK¿J_ b\`am f b | ?  j ¼ @ ‰a‰Å Í [^_ ] q mK` f b\` nÞÑ ×\mÇ`‡d fh[ m g _½o\_ q _ [^_c] ` g1n d } d7Å p }kb\`Ì`l} Z\[ _ g1¾ _ÚáBÆÅ Ý }k`a×\moBz} [ } [^_7] } Ø n mÇ`Ï_ n _c` q+Ä^qcn _ ` Z1[af^q ×\_c` qcf ¿"¿"_,` fhnKg dlm f b\`zo Ñ g b q _ [ d }kmKb Üh[ }ko gu_ ] Üh[ P™›š | ? Ýœ @ ‰+Å5r@} o _c] ¿ f b\`Ïd [ }Údam f b g dam n mK`a_ g b1_ Z\[ÏfhZ\[ m _ ] d _ ] Î9fk[ dl_o\_ n } [^_ ] Ühg\n } [ mGd _E] ~ nÞÑ _+Ù@mK`Ïdl_ b q _Jo\_ F Ø Î9f b q dam f b\` qcf bed [ fh n+_ ] _c` Å Í } [in }'` g mKda_ká€ÛNÅ1_ j × fhg dÌ_ d syÅQr1} j\j }k× fhj damÇb [ _cbed q _+dada_ .

(14) ÜN_c] b _ ] [ } n mÇ`a}Údlm f b q f ¿J¿"_ q f b\` _ ] g _cb q _'o1m [ _ q da_ o\_ n }o _ ] €b1mKdlm f bo\_ n } [^_ ] Ühg\n } [ mKd _] _+d o g‚Î9fk[ ¿J} n mK`a¿"_o\_ n }'dl× _ ] fh[ mK_o1_c` E؇ f o g\n _c` | ? ÆÅ r j @ á ? r j À @ ‰+Å r f mKd¿œ}ÚmÇbedl_ b€}kbed   |  x"%$%$%$&"  ‰J~  =   g b\_} Z\Z\n m q }Údam f bÆ}kb€} nKÄ dlm ^g _ b g1nÇn _ } Ð nÞÑ fh[ m Ü mÇb\_Úá$o _ ] €b1mÇ`a`a}kbed g b\_imÇbeda_ [ `Ï_ q dlm f b q f ¿ Z\nÞ_+Ð dl_“_ b X ÅhÊÌ} Z\Z _ nÇf b\` g _ Ë _ p Åkƒ,Åe}k`Ï` f^q mK_ }-Ð :  ­~ |  [ _co " X ‰ = |  " X ‰ g b\_ j\[ }Údlm f b qcf bdamÇb g _ nKf@q } n _ ¿J_ bd d [ m ¾ mM} n _'}kb\} nÇfhÜkg _ } Ð q _ nÇn _'o\_"Ó1ÅÉm n b fh[nÇfh[ ` g _  _ `Ïd n mK`a`Ï_ | ? Ë _  A@ á ? b @ ‰+Å €b o Ñw_+] d g o1mÇ_ [Bn _. Z&fknKÄ b f  ¿"_3o\_ È _ [ b\`Ïda_cmÇbo\_ n } [ _ `Ïd [ m q dlm f bo1_O: }

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(94) 3v b g dlm n mÇ`a}kbed g b\_ _ ] g }Údam f b Î9f b q dam f b1b\_ nKn _io€}kb1` E ) ? ÀR4 :  " G @ :  K [^_7] } n mÇ`a}kbed n _ Z&f Ø nKÄ b f  ¿"_#o\_ È _ [ b1`Ïdl_ mÇbEo1_ :" }k`a` f@q m _ ] }›Ð D›á f b q f b\`‡d }Úda_z}kmK` _c] ¿"_cbed g _ F |  N | D‚‰ :  K " G ‰ o\m ¾ mÇ`Ï_ F | D :  K " G ‰+Å p Ñ } g d [ _ Z } [ d7á q f b\`ÏmÇo _ ] [af b\` nÒÑw_ ] ^g }Údlm f b Î9f b q dam f b1b\_ nKn _ ` g m ¾ }kbedl_ | àe‰ F |  N | D‚‰ :& K " G ‰  N | D‚‰ :& K ML $  N | D‚‰ :& KHN  fBg Ð L T U? G @ Å* Z\[c_ Ð ` o\m ¾ mÇ`Ïm f bÆ_ g\q n mKo\mÇ_ b\b\_ Z } [ #"%$%$‡$7"  áNo1_c` qcf _+* q mÇ_cbeda` o\_ nÞÑ fhZ{_ ] [ }Údl_ g\[ L o€}Úb\`=` f b _ ] q [ mKd g\[ _»} ¾ _ q»q f _#* q mÇ_ bedl` }™ Ð o [af mGdl_káÌm n ` Ñw_ ] qc[ mGd L  "  G  G @ @ fBg Ð T U? _ d T U? _c`ÏdœmÇb\o _ ] Z _cb\o€}Úbdœo\_  Å r1}kb\‚ # `  Z _ ‚ [ dl‚ _+ o\_ Ü*_c] b _ ] [ } ‚ n mKd _Ú] á#b fhg ` Z&fhg@¾hf b\`œo f b q ` g\Z\Z5f `Ï_ [ g _=o\}kb\` #nÒ"%Ñ mK$%o\$%_c$7be" damKd _ ] | à‰á nÞÑ fhZ{_ ] [ }Úda_ g\[ L¨} Z\Z } [ dlmÇ_ bed } Ð !  x"%$%$‡$ " 9' 0325462 ‡"‡$%$%$7" 25462  8 ? G @ Å . T  ' PR? G @ á n _da_ [ ¿J_ qcN f b1`Ïd }Úbdo\_ L ¾^g qcf ¿J¿"_ fhZ{_ ] [ }Údl_ g\[ _cb r f mKd} nKfh[ ` L | 25462  ‰ "%$%$‡$ " | 25462  ‰ } Ð qcf _+* q mÇ_cbeda`o€}kb\`  ' P!? G @ Åzt n _c`‡d¿œ}kb1m Î _c`‡dl_ ^g _ nÞÑ f b . o€}Úb\` nÒÑ mKo\_cbedamKd _ ] | à‰+Å5s f ¿"¿"__ b €b nÒÑ }Úb\b g\n }Úda_ g\[ o€}Úb\` Z _ g d [ _c¿ Z\n } q _ [ L Z } [ L¨ G |  ' PR? @ o\_  D‚‰ :  K q fÔ ˜Gb q mKo\_E} ¾ _ qEq _ nÇg mo\_–D :  K á5b fhg `y_cbo _c] o g mÇ` f b\`,} nKfh[ ` g _ F |  N | D‚‰ :  K " G N ‰u_c`‡d g b‚¿ g\n dam Z\n _ o\_ F | D :  K " G ‰+Å v3b qcf b1` _ ] g _ b q _Úá F |  N | D‚‰ :  K " G ‰u_c`Ïd j mK_cb _ ] Ü } nu} Ð F | D :  K " G ‰Å ) #+*,*,#  - ZAlmj /"9^&b lm^ d b# j b#gxaŽlm^bq b3 2 Z!h!ZA^ih4  / '   ! " / ' 0325462 %"‡$%$%$ 2 4€2  8 b#j ^&ZAj ZA^ih E  / ' [ b   / ' 0325462 / 8 kacZ d 9[ b @<ZA[ ZA^&ZAacb E   ! " / ' 3  [ ZAgqh 0 Y<Z=9g”j Z=9jOb# [b# acb#^<j D TE ^&u n#YWYin6gxjkb#^5n6^<j YinAh sn [onU: kj ZAg h#l3ZA^ d b)E 0 F | DJ: K " G ‰f F |a| DJ4 | / V :ɉa‰ / K " G ‰ 0 Z  s DJ4 | / V : ‰#TtE  / ' ?HÀ!4 / V : @ 4€E  / ' d

(95) b h#loy6^&b-[on}p#[onAhqh!b d b`DJ4 | / V :ɉ3 2 g b

(96)  I6b3

(97) [ }  q _»} gIn _c¿"¿"_²ÀkÅKÀhÅGÀhÅ ¼1á F |a| DJ4 | / V :ɉω / K " G ‰ qcf7ԘKb q mÇo\_ } ¾ _ q n _ Z&f Ø nKÄ b f  ¿"_o\_ È _ [ b1`Ïdl_ mÇb o\_ | DJ4 / ‰v: K T | E  /  ' ?HÀ!4 /  @ 4€E  /  ' ‰‡? ÀR4S: " G @ : K | _cb Î }kmGØ `l}kbed n _ q ׀}kb Ü _c¿"_cbedo\_ qcf^fh[ o f b\b _ ] _c` /1  / V :ɉ+Å p Ñ } g d [ _ Z } [ d7á _ b Z\[af^q5_ ] o€}kbed qcf ¿"¿J_o\}kb\` n } Z\[ _ g1¾ _o g)n _c¿"¿J_ Z1[^_ ] q5_c] o\_ bed7á f b _ ] dl} j\n mKd g _ n _c` Z5fhnKÄ b f  ¿J_ ` F |Ï| DJ4 / ‰ : K " G ‰u_ d F | DJ: K " G ‰u` f bed _ ] Ü } g Ù&Å p Ñ fTgÐ nÒÑ }Ú`a`a_ [ dam f bÉÅ . . . . . . . . . FJGIFJG. R`c N P /P N RUc T R`c [ L N 7[ ORUN NSR`V P\MOaJT7N

(98)  . . 

(99).

(100). . . r f mKd   g b ¾kf mÇ`ÏmÇb€} Ü _ o\_ nÒÑ fk[ m Ü mÇb\_ÚÅ x fhg `b f dl_ [af b1`—) | [ _c` Z Å%)5‰ n _ Î }kmÇ` q _7} g o\_ ` Î9f b q dlm f b\`× fhnÇf ¿ fh[ÏZ ×\_c` | [ _c` Z Å fhZ{_ ] [ } dl_ g1[ `yo1m _ ] [ _ bedlmÇ_ n `l‰ ` g\[  á5o\_  j\[ _ } Ð nÞÑ fh[ m Ü mKb\_ | [ _c` Z Å J‰+Å r f mÇ_ bd :-~W =  á g b\_ Î9f b q dlm f b× fhnÇf ¿ fh[ÏZ ×\_b f b qcf b\`Ïdl}kbedl_ká€b g\nKn __cb X á1_+d E g b –1؇ f o g\n _ × fhnKf b f ¿"_kÅ p }Úb\` q _ Z } [ } Üh[ } Z ×\_káÚb fhg `>o f b\b f b1` ^g _ n g _ ` [^_ ] ` g\n d }Úda` [ _ n }Údam Î `>} g ÙE`Ï_ q dlm f b\` DJ: K á D T Eºáuo g U? G @ Øw f o g\n _UE ?HÀR46: " G @ : K Åzx fhg ` [ } Z\Z _ nÇf b1`œo Ñ } j5fh[ o­o\_ ` À¼.

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