<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f3.xsl"?>
<top_article>
 <mrnumber>MR1815469</mrnumber>
 <author>Badora, Roman</author>
 <author_utf8>Roman BADORA</author_utf8>
 <title>On the d'Alembert type functional equation in Hilbert               algebras</title>
 <journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
 <volume>43</volume>
 <year>2000</year>
 <page>405--418</page>
 <url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol43/fe43-3-2.pdf</url_pdf>
 <url_infty_pdf>http://fe.math.kobe-u.ac.jp/FE/no-infty-pdf.pdf</url_infty_pdf>
 <mathsci_link> http://www.ams.org/mathscinet-getitem?mr=MR1815469</mathsci_link>
<fesi_info>
  <FILE>43-405</FILE>
  <YEAR>2000</YEAR>
  <TITLE>On the d'Alembert Type Functional Equation in Hilbert Algebras</TITLE>
  <AUTHOR>Roman BADORA</AUTHOR>
  <AUTHOR_utf8>Roman BADORA</AUTHOR_utf8>
</fesi_info>

<references>

<book>
<bibitem>1</bibitem>
<author>Acz&#233;1, J.; Dhombres, J.</author>
<booktitle>Fonctional equations in several variables</booktitle>
<publisher>Cambridge University Press, Cambridge</publisher>
<year>1989</year>
<mr>MR1004465</mr>
</book>

<article>
<bibitem>2</bibitem>
<author>Chojnacki, W.</author>
<title>Fonctions cosinus hilbertiennes born&#233;es dans les groupes commutatifs localement compacts</title>
<journal>Compositito Math.</journal>
<vol>57</vol>
<year>1986</year>
<page>15-60</page>
<mr>MR0817295</mr>
</article>

<article>
<bibitem>3</bibitem>
<author>Dixmier, J.</author>
<title>Les moyennes invariantes dans les semi-groupes et leurs applications</title>
<journal>Acta Sci. Math., (Szeged)</journal>
<vol>12A</vol>
<year>1950</year>
<page>213-227</page>
<mr>MR0037470</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Fattorini, H. O.</author>
<title>Uniformly bounded cosine functions in Hilbert space</title>
<journal>Indiana Univ. Math. J.</journal>
<vol>20</vol>
<year>1970</year>
<page>411-425</page>
<mr>MR0267417</mr>
</article>

<book>
<bibitem>5</bibitem>
<author>Fattorini, H. O.</author>
<booktitle>Second order Linear Differential Equations in Banach spaces</booktitle>
<publisher>Noth Holland, Amsterdam-New York</publisher>
<year>1985</year>
<mr>MR0797071</mr>
</book>

<other>
<bibitem>6</bibitem>
<raw_data>Ger, R., Christensen measurability and functional equations, Berichte der Mathematisch-Statistischen Sektion in der Forschungsgesellschaft Joanneum-Graz, Bericht Nr. 289 (1988)</raw_data>
<mr>MR1012745</mr>
</other>

<article>
<bibitem>7</bibitem>
<author>J&#228;rai, A.</author>
<title>Remark 23</title>
<journal>Aequationes Math.</journal>
<vol>51</vol>
<year>1996</year>
<page>178</page>
</article>

<article>
<bibitem>8</bibitem>
<author>Kannappan, Pl.</author>
<title>The functional equation $f(xy)+f(xy^{-1})=2f(x)f(y)$ for groups</title>
<journal>Proc. Amer. Math. Soc.</journal>
<vol>19</vol>
<year>1968</year>
<page>69-74</page>
<mr>MR0219936</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>Kurepa, S.</author>
<title>Uniformly bounded cosine function in a Banach space</title>
<journal>Math. Balkanica</journal>
<vol>2</vol>
<year>1972</year>
<page>109-115</page>
<mr>MR0320819</mr>
</article>

<book>
<bibitem>10</bibitem>
<author>Naimark, M. A.</author>
<booktitle>Normed Rings</booktitle>
<publisher>Noordhof, Groningen</publisher>
<year>1964</year>
<mr>MR0355601</mr>
</book>

<article>
<bibitem>11</bibitem>
<author>O'Connor, T. A.</author>
<title>A solution of the functional equation $\phi(x-y)=\sum_1^na_j(x)\overline{a_j(y)}$ on a locally compact Abelian group</title>
<journal>J. Math. Apal. Appl.</journal>
<vol>60</vol>
<year>1977</year>
<page>120-122</page>
<mr>MR0454444</mr>
</article>

<book>
<bibitem>12</bibitem>
<author>Rickard, C. E.</author>
<booktitle>General Theory of Banach Algebras</booktitle>
<publisher>D. Van Nostrand Company, Inc., Princeton-Toronto-New York</publisher>
<year>1960</year>
<mr>MR0115101</mr>
</book>

<article>
<bibitem>13</bibitem>
<author>Rukhin, A. L.</author>
<title>The solution of the functional equation of d'Alembert's type for commutative groups</title>
<journal>Internat. J. Math. Math. Sci.</journal>
<vol>5</vol>
<year>1982</year>
<page>315-335</page>
<mr>MR0655518</mr>
</article>

<other>
<bibitem>14</bibitem>
<raw_data>Stetkaer,. H., Functional equations and spherical functions, Aarhus Univ. Preprint Series No. 18 (1994)</raw_data>
<mr>MR1295092</mr>
</other>

<article>
<bibitem>15</bibitem>
<author>Sz&#233;kelyhidi, L.</author>
<title>Functional equations on abelian groups</title>
<journal>Acta Math. Acad. Sci. Hungar</journal>
<vol>37</vol>
<year>1981</year>
<page>2235-243</page>
<mr>MR0616892</mr>
</article>


</references>
</top_article>
