- Email: [email protected]
Reply of Professor M. Valdivia
xix
REPLY OF PROFESSOR M. VALDIVIA The Honourable Minister of Culturc, I':tlucat.ioii, Sciencc of tlic Govcriimcnt of Valencia, Your Exccllcncy, the Gcncral Dircctor of IJiiivcrsitics in tlic Govcrrirncnt of Valencia, Your Exccllcncy, Rector of tlic Ilnivcrsity of Valc!iiciiL, Your Exccllency, ltcctor of tlic 'lidiliolo)giciiI IJiiivcrsity of Valciicia, Excellcnt Sirs, IIonoiirahle 1,atlirs aiicl ( ~ ~ i i t . l ~ ~ i iDcnr i ~ ~ i iColleagucs , and Ricnds: First of all, I want to thank the iiislitutions who, through tlicir ofiicial and financial support, havo ma.& possible this Iioniiig(1 for wliicli I ain liciartily indchted: thc Covernincnt of the S h t c of Valencia, the Ministry of I':tlucat.ioii aiitl Scicncc, tlic Valcncian Ministry of Culturc, Education antl Sciciicc. tlio Iliiivc~sityof Viilciicia, tlic 'I'cchnological Univcrsity of Vitlcncia, tlic k'acnlty ~ lhint ' lic1iii1tnics9tlic Scliool of Architccturc, tlic Scliool of 'I'clecomiiiuniratioris, tlic I)qmrtiii(!iit. o f :\ppli(d Xliit Iiriiiittics of tlic Teclinological Ilniversity of Valeiicia and tlic- I)cl)i1rtiiit.iit of i\li1tli~:il1iiticalAnalysis of the University of Valencia.
I want to tliarik tlic oficial iiistitutioiis illid. i i i o r c xpccilicidly, tlicir appointed rcprcscntatives at this cvcnt, not oiily for tlicir cdli~l)o~ilti<~i~ iii this celrbration, but also for the cnorrno~ssupport tlicy arc giving to ctliiriitioil iliitl rcscarcli for tlic benefit of Univcrsity, Sciencc niitl Culture. For scv(irii1 ycars now tlic conditions uiitlc.r which rcwiiircli is beiiig tloiic Iiavc: irnprovccl quite obviously antl they coiitiiiuc. to i~iiprovc.'L'linnks to this iicw situation, niathematiciaiis caii establish contact and ciiii cooi)cwtmc wit Ii scicwtist.s in tlic wliole world travclliiig licrc and there antl cloiiig joiiit work. I I I tlic Stiit.(*of Villc~iiciawe Iiavc iiow rcachctl a niathemnt.ical levd which is vc8r) rl!SI)l'Ct.iIlJh.' i\iitl wiilclg rcsp(!ctcd. ]hit we must rcmgnize tliat this is not only cluc to tlic ( 4 i ) r t of tlic! iiiatlic.iiiatic.iaIis, but also clue to the strong support of the inutitutioiis. It. is i i o ~by cliaiicc that soiiic- o f tlic anthritics who honour us today by tlicir pr(w-iic(i Iic~rci ill'(' idso j)rol'essors aiitl rcxoiarcliars. Thcy liavc known vory wcll how iiiiprtiliit r(:st.ildi illid cdiicnt.ioii itr(' for socicty aiitl IIWC ac.totl accordingly, liclpirig us iii o i i r tiislts. liiiitl o f Vnlciicia and wa.. rcccivctl corTiventy-livc ycars ago 1 arrivcxl iii this Ii0spiIitl)l~~ dially aid warmly hy niy collc!aguc-s iii tlic l'oriiiinr lhciilty of Sciciice. 1 came with tlic iriissioii to cxplaiii 1ilathci1iihti(:s i i i tIi(*Srv:tioii ol' I'liysics iiiitl latcr o i i I was iii cliargc! of Mathcnia t ical Analysis in t tic! Ihcii I ty. 'I'liosc!\wrc! wry cli I liciilt t iincs profcssionally. W e did not have mathematical jouriials. 'I'lic chair to wliicli I was appointcd could not alford to buy books. 1 wcnt to Midrid to s(xi tlic CciicriLI Dircxtor of our Ministry to ask hini for hclp, and hc offcrctl me 100.000 ~ i c s c t a sfor IJOO~S. 181-iiic., this was the actual beginning of rnathcmatics in the: I'kciilty.
During those twenty-five yosrs, all iiiy Lcidiiiig a i i c l rcsc!arcli w w carried out in thc Univcrsity of Valencia as wcll as iii tlic li!cliiiological University or Valencia wliicli I joiiicd at the same moment wlicn 1 caiiic IICTC, first as ill1 Associatc Profcssor, latcr on as Full Professor for Matliciiiat,ics 1 i n 11~-Scliool of Agricdttirirl Enginwring. It was an honour for me to collaborate in tlic foriiiirtioii of tliv 'li~cliiiolo~i~i~l lliiiversity of Valciicia, wlicrc my work was carried out in tlic Icgiiiiiing by giviiig lcctiirrs in tlic Scliools of Architecturc
xx
Reply of Professor M. Valdivia
and Agriculture and then by tliiwtiiig t IIC I)c~]xirtniriitof hfatliciiiatics of tliat University.
I must say licrc t h a t I a m very p r o u d of lily original career as a i l agricultural engineer; as sucli, I remembcr with grcat plcasurc tlic tiiiic wlien I \vorlictl in hlatlrid, giviiig classes of genetics, physics and clieiiiistry, tlicii i n rational mechanics and mat,hematics. I used to say that I was a mathcmaticiaii of late vocation: I was 31 ymrs old wlien I enrolled iii tlie Faculty of Mathematics in hIadritl. During my first years at the TJniversity ol Valcncia, an important event, occurred, the foundation of the Faculty of h’latlicmatics, i i i wliicli I participatcd and contributcd from t h a t time on by explaining scvcral topics witli the aim of consolidating tlie Faculty. Some of you, who have worked togetlier with nit, studied in Valrncia a t t h a t time and hence remcmher how many tlilficultks we uscd t o liave. Concerning my research, the first years \ v c w a t.iiiic of isolation and solitude. 1 had finished my Doctoral Thesis in hlatlritl, under tlic tlircction of I). Ricardo San Juan, on t h e classical theory of integratioii, hut I>. Ricardo iiisistctl tliat I sliould cliaiige topics. Oiice I was in Valericia, I t,liouglit it \ v o i i l t l IJC iiit.crc,stiiig to do iiivcstigations i r i Fiiiictiorial Analysis. I got a book on locally convex spiicc;s, tlic one of I’rofcssor Kotlie, a pcrsoii well-known t o many of you, for w l i o i i r 1 always had great. i ~ ~ s p c cantl t deep affection. I takc this opportiinit,y t,o say tliat, I will always Iiccll his mciiiory in highest regard. Kothc’s monograpli, written in Germail, was tliflicult for iiic to rcwtl, a i i d it took m e a long time to study it with the help of a clict.ioii;iry. 1,iLtcr 0 1 1 , tlicre apprarctl, like a miracle, two books in English which were iiiy last resort: tlic Imolts of Profcssors Scliacfcr and IIorvAtli, rcspcctively. Wlien I studied t l i c i i i , I started piililishing some articles in the Rcvista d e la Academia d c Cicncias, in Madrid, yet wit.liorit bring a l ~ kt,o check wit,li aiiybotly if they contained intcrcsting rcsult,s. I j u t it was I’rofcssor IIorvAtli wlio savcd me from this situation. Before I worked with Sail Juaii, I’rol‘essor 1lorvdt.li l i a t l visited Madrid, invited by D. Ricardo, and given a course o i i quasianalytic cla.sses, and from t h a t point on they both liad kept in contact and cschangccl letters. D. Ricardo wrote him allout me, and t h e answer did not takc long: I rcceivetl froin I,ii.gc, scnt hy De Wiltle, his famous doctoral thesis. Later on, Profrssor Garnir, wliosc~i i i r i n o r y Iias always brcn in my highest regard, scnt mc an invitation to attend a congress wliicli was organized a t Likgc. I went tlierc arid I met Professor Kotlie and ot.licr Ii1at,lie1iiiil iciaiis i n t.lie ficsltl. This was, i n my opiiiioii, the beginning of mathematics a t i i u iiitcriiational lcvel in our universities a t Valcncia. Consequently, wc owe many tliiIlllis to Prol’(wor I~Iorviitli.We liave just heard his lecture on my work. I cannot firid tlic proper \vortls to express Iiow gratcful I feel. I can only offcr hiin my fricntlship, wliicli lit> drcirtly has, CVCII t l o c y o i . antl closer, i f possible.
I fccl the samc way a.horit t~lic: 1’1.ol’c~ssorsa i i t l 17ricnds Josi. Uonet, 1i;laus Dierstcdt and hlanucl hlacstre. I do not I ~ I I O W Iiow to adtlrcss them at this occasion, b u t they sliould
know tliat my thanks are sincere a n d cordial.
At the same time I slioultl c x p r ( w iiiy spoci;il gratitude for the members of tlie supporting committee: Professors Pablo (ialiiiclo, Ihiiiiiigo Garcia, RIauucl Lcipez I’clliccr, Viccrit,e hlori t csirios arid Josd Luis Sail tos .
Many t h a n k s to all t,liose w l i o a r r
iii
t l i c autlicvice now: friends, companions, collcagucs,
Reply of Professor
prcstigious mat,licmaticians wlio
lioiioiir I I K ,
M. Valdivia
xxi
by t,licir pt’(~sc~icc.
Before I firiisli I have to say that Futictioiiid Atialysis i n tlic Community of Valcncia goes further and furthcr thanlts to tliosc youiig itiatlicttiiitiCi~iiiswlio work in our Univcrsitics: In spitc of thcir youth, some of t l i c i i i ar(t \ v ( ~ l l - l i i l o \ v i ~ititt!rriiitiotially. I n order to reach this situation, many hours of \+rorli, pontlcriiig aiid cfrort werc necessary. J u s t as Laurent Schwnrtz said in the prcface to oiic o f liis I)ool;s: “‘l’licrc is no mathcniatics without tcars.”
I would also like to mention hliiriii ‘I‘crcsa, my wife, who has always lieen my helper, supporting m e a t cach moment it1 iny work aiid dctlicatiiig Iicrsclf, togctlicr with mc, to the service of the IJnivcrsity of Valclicia. tluriiig tlicsc twtrtit,y-five years. And that’s all, I only want to cspIcss iiiy oniotioii and gratitudc with a vcry simple sentencc: Thanks to all of you, my h u t is with you. I’eiliscola, October 22, 1990
xxii
Professor M. VaMivia
Professor M . Valdivia during the visit to the castle of Peniscola
REPLY OF PROFESSOR M. VALDIVIA The Honourable Minister of Culturc, I':tlucat.ioii, Sciencc of tlic Govcriimcnt of Valencia, Your Exccllcncy, the Gcncral Dircctor of IJiiivcrsitics in tlic Govcrrirncnt of Valencia, Your Exccllcncy, Rector of tlic Ilnivcrsity of Valc!iiciiL, Your Exccllency, ltcctor of tlic 'lidiliolo)giciiI IJiiivcrsity of Valciicia, Excellcnt Sirs, IIonoiirahle 1,atlirs aiicl ( ~ ~ i i t . l ~ ~ i iDcnr i ~ ~ i iColleagucs , and Ricnds: First of all, I want to thank the iiislitutions who, through tlicir ofiicial and financial support, havo ma.& possible this Iioniiig(1 for wliicli I ain liciartily indchted: thc Covernincnt of the S h t c of Valencia, the Ministry of I':tlucat.ioii aiitl Scicncc, tlic Valcncian Ministry of Culturc, Education antl Sciciicc. tlio Iliiivc~sityof Viilciicia, tlic 'I'cchnological Univcrsity of Vitlcncia, tlic k'acnlty ~ lhint ' lic1iii1tnics9tlic Scliool of Architccturc, tlic Scliool of 'I'clecomiiiuniratioris, tlic I)qmrtiii(!iit. o f :\ppli(d Xliit Iiriiiittics of tlic Teclinological Ilniversity of Valeiicia and tlic- I)cl)i1rtiiit.iit of i\li1tli~:il1iiticalAnalysis of the University of Valencia.
I want to tliarik tlic oficial iiistitutioiis illid. i i i o r c xpccilicidly, tlicir appointed rcprcscntatives at this cvcnt, not oiily for tlicir cdli~l)o~ilti<~i~ iii this celrbration, but also for the cnorrno~ssupport tlicy arc giving to ctliiriitioil iliitl rcscarcli for tlic benefit of Univcrsity, Sciencc niitl Culture. For scv(irii1 ycars now tlic conditions uiitlc.r which rcwiiircli is beiiig tloiic Iiavc: irnprovccl quite obviously antl they coiitiiiuc. to i~iiprovc.'L'linnks to this iicw situation, niathematiciaiis caii establish contact and ciiii cooi)cwtmc wit Ii scicwtist.s in tlic wliole world travclliiig licrc and there antl cloiiig joiiit work. I I I tlic Stiit.(*of Villc~iiciawe Iiavc iiow rcachctl a niathemnt.ical levd which is vc8r) rl!SI)l'Ct.iIlJh.' i\iitl wiilclg rcsp(!ctcd. ]hit we must rcmgnize tliat this is not only cluc to tlic ( 4 i ) r t of tlic! iiiatlic.iiiatic.iaIis, but also clue to the strong support of the inutitutioiis. It. is i i o ~by cliaiicc that soiiic- o f tlic anthritics who honour us today by tlicir pr(w-iic(i Iic~rci ill'(' idso j)rol'essors aiitl rcxoiarcliars. Thcy liavc known vory wcll how iiiiprtiliit r(:st.ildi illid cdiicnt.ioii itr(' for socicty aiitl IIWC ac.totl accordingly, liclpirig us iii o i i r tiislts. liiiitl o f Vnlciicia and wa.. rcccivctl corTiventy-livc ycars ago 1 arrivcxl iii this Ii0spiIitl)l~~ dially aid warmly hy niy collc!aguc-s iii tlic l'oriiiinr lhciilty of Sciciice. 1 came with tlic iriissioii to cxplaiii 1ilathci1iihti(:s i i i tIi(*Srv:tioii ol' I'liysics iiiitl latcr o i i I was iii cliargc! of Mathcnia t ical Analysis in t tic! Ihcii I ty. 'I'liosc!\wrc! wry cli I liciilt t iincs profcssionally. W e did not have mathematical jouriials. 'I'lic chair to wliicli I was appointcd could not alford to buy books. 1 wcnt to Midrid to s(xi tlic CciicriLI Dircxtor of our Ministry to ask hini for hclp, and hc offcrctl me 100.000 ~ i c s c t a sfor IJOO~S. 181-iiic., this was the actual beginning of rnathcmatics in the: I'kciilty.
During those twenty-five yosrs, all iiiy Lcidiiiig a i i c l rcsc!arcli w w carried out in thc Univcrsity of Valencia as wcll as iii tlic li!cliiiological University or Valencia wliicli I joiiicd at the same moment wlicn 1 caiiic IICTC, first as ill1 Associatc Profcssor, latcr on as Full Professor for Matliciiiat,ics 1 i n 11~-Scliool of Agricdttirirl Enginwring. It was an honour for me to collaborate in tlic foriiiirtioii of tliv 'li~cliiiolo~i~i~l lliiiversity of Valciicia, wlicrc my work was carried out in tlic Icgiiiiiing by giviiig lcctiirrs in tlic Scliools of Architecturc
xx
Reply of Professor M. Valdivia
and Agriculture and then by tliiwtiiig t IIC I)c~]xirtniriitof hfatliciiiatics of tliat University.
I must say licrc t h a t I a m very p r o u d of lily original career as a i l agricultural engineer; as sucli, I remembcr with grcat plcasurc tlic tiiiic wlien I \vorlictl in hlatlrid, giviiig classes of genetics, physics and clieiiiistry, tlicii i n rational mechanics and mat,hematics. I used to say that I was a mathcmaticiaii of late vocation: I was 31 ymrs old wlien I enrolled iii tlie Faculty of Mathematics in hIadritl. During my first years at the TJniversity ol Valcncia, an important event, occurred, the foundation of the Faculty of h’latlicmatics, i i i wliicli I participatcd and contributcd from t h a t time on by explaining scvcral topics witli the aim of consolidating tlie Faculty. Some of you, who have worked togetlier with nit, studied in Valrncia a t t h a t time and hence remcmher how many tlilficultks we uscd t o liave. Concerning my research, the first years \ v c w a t.iiiic of isolation and solitude. 1 had finished my Doctoral Thesis in hlatlritl, under tlic tlircction of I). Ricardo San Juan, on t h e classical theory of integratioii, hut I>. Ricardo iiisistctl tliat I sliould cliaiige topics. Oiice I was in Valericia, I t,liouglit it \ v o i i l t l IJC iiit.crc,stiiig to do iiivcstigations i r i Fiiiictiorial Analysis. I got a book on locally convex spiicc;s, tlic one of I’rofcssor Kotlie, a pcrsoii well-known t o many of you, for w l i o i i r 1 always had great. i ~ ~ s p c cantl t deep affection. I takc this opportiinit,y t,o say tliat, I will always Iiccll his mciiiory in highest regard. Kothc’s monograpli, written in Germail, was tliflicult for iiic to rcwtl, a i i d it took m e a long time to study it with the help of a clict.ioii;iry. 1,iLtcr 0 1 1 , tlicre apprarctl, like a miracle, two books in English which were iiiy last resort: tlic Imolts of Profcssors Scliacfcr and IIorvAtli, rcspcctively. Wlien I studied t l i c i i i , I started piililishing some articles in the Rcvista d e la Academia d c Cicncias, in Madrid, yet wit.liorit bring a l ~ kt,o check wit,li aiiybotly if they contained intcrcsting rcsult,s. I j u t it was I’rofcssor IIorvAtli wlio savcd me from this situation. Before I worked with Sail Juaii, I’rol‘essor 1lorvdt.li l i a t l visited Madrid, invited by D. Ricardo, and given a course o i i quasianalytic cla.sses, and from t h a t point on they both liad kept in contact and cschangccl letters. D. Ricardo wrote him allout me, and t h e answer did not takc long: I rcceivetl froin I,ii.gc, scnt hy De Wiltle, his famous doctoral thesis. Later on, Profrssor Garnir, wliosc~i i i r i n o r y Iias always brcn in my highest regard, scnt mc an invitation to attend a congress wliicli was organized a t Likgc. I went tlierc arid I met Professor Kotlie and ot.licr Ii1at,lie1iiiil iciaiis i n t.lie ficsltl. This was, i n my opiiiioii, the beginning of mathematics a t i i u iiitcriiational lcvel in our universities a t Valcncia. Consequently, wc owe many tliiIlllis to Prol’(wor I~Iorviitli.We liave just heard his lecture on my work. I cannot firid tlic proper \vortls to express Iiow gratcful I feel. I can only offcr hiin my fricntlship, wliicli lit> drcirtly has, CVCII t l o c y o i . antl closer, i f possible.
I fccl the samc way a.horit t~lic: 1’1.ol’c~ssorsa i i t l 17ricnds Josi. Uonet, 1i;laus Dierstcdt and hlanucl hlacstre. I do not I ~ I I O W Iiow to adtlrcss them at this occasion, b u t they sliould
know tliat my thanks are sincere a n d cordial.
At the same time I slioultl c x p r ( w iiiy spoci;il gratitude for the members of tlie supporting committee: Professors Pablo (ialiiiclo, Ihiiiiiigo Garcia, RIauucl Lcipez I’clliccr, Viccrit,e hlori t csirios arid Josd Luis Sail tos .
Many t h a n k s to all t,liose w l i o a r r
iii
t l i c autlicvice now: friends, companions, collcagucs,
Reply of Professor
prcstigious mat,licmaticians wlio
lioiioiir I I K ,
M. Valdivia
xxi
by t,licir pt’(~sc~icc.
Before I firiisli I have to say that Futictioiiid Atialysis i n tlic Community of Valcncia goes further and furthcr thanlts to tliosc youiig itiatlicttiiitiCi~iiiswlio work in our Univcrsitics: In spitc of thcir youth, some of t l i c i i i ar(t \ v ( ~ l l - l i i l o \ v i ~ititt!rriiitiotially. I n order to reach this situation, many hours of \+rorli, pontlcriiig aiid cfrort werc necessary. J u s t as Laurent Schwnrtz said in the prcface to oiic o f liis I)ool;s: “‘l’licrc is no mathcniatics without tcars.”
I would also like to mention hliiriii ‘I‘crcsa, my wife, who has always lieen my helper, supporting m e a t cach moment it1 iny work aiid dctlicatiiig Iicrsclf, togctlicr with mc, to the service of the IJnivcrsity of Valclicia. tluriiig tlicsc twtrtit,y-five years. And that’s all, I only want to cspIcss iiiy oniotioii and gratitudc with a vcry simple sentencc: Thanks to all of you, my h u t is with you. I’eiliscola, October 22, 1990
xxii
Professor M. VaMivia
Professor M . Valdivia during the visit to the castle of Peniscola