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  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-15184</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/15184</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Статьи</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Articles</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">On some inequalities established when presenting the Schwartz-Poincare - Steklov method and also encountered in solving many minimal problems</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>О некоторых неравенствах, устанавливаемых при изложении метода Schwartz-Poincare — Стеклова и встречающихся также при решении многих минимальных задач</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Krylov</surname>
            <given-names>N. M.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Крылов</surname>
              <given-names>Н. М.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Krylov</surname>
              <given-names>N. M.</given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru"> (Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en"> (Russia)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="1916-12-01">
        <day>01</day>
        <month>12</month>
        <year>1916</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>1916</year>
      </pub-date>
      <volume>6</volume>
      <issue>1</issue>
      <fpage>10</fpage>
      <lpage>14</lpage>
      <history>
        <date date-type="received" iso-8601-date="1916-06-30">
          <day>30</day>
          <month>06</month>
          <year>1916</year>
        </date>
        <date date-type="accepted" iso-8601-date="1916-08-14">
          <day>14</day>
          <month>08</month>
          <year>1916</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="1916-12-01">
          <day>01</day>
          <month>12</month>
          <year>1916</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="ru">© 1916 Н. М. Крылов</copyright-statement>
        <copyright-statement xml:lang="en">© 1916 N. M. Krylov</copyright-statement>
        <copyright-year>1916</copyright-year>
        <copyright-holder xml:lang="ru">Н. М. Крылов</copyright-holder>
        <copyright-holder xml:lang="en">N. M. Krylov</copyright-holder>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="ru">
          <license-p>Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0)</license-p>
        </license>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="en">
          <license-p>This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/15184">https://pmi.spmi.ru/pmi/article/view/15184</self-uri>
      <abstract xml:lang="ru">
        <p>В различных математических исследованиях, связанных с вопросом о существовании минимума весьма часто бывает полезно, как мы постараемся ниже показать, приложение того основного соотношения в теории тригонометрических рядов, которое было названо проф. В. А. Стекловым уравнением замкнутости и обобщено им для многих других систем ортогональных функций, встречаю­щихся в анализе и математической физике.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>In various mathematical studies related to the question of the existence of a minimum, it is often useful, as we will try to show below, the application of that basic relationship in the theory of trigonometric series, which was named by Prof. V. A. Steklov as a closed equation and generalized by him for many other systems of orthogonal functions found in analysis and mathematical physics.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>-</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body/>
  <back>
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      <ref id="ref1">
        <label>1</label>
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        <label>5</label>
        <mixed-citation xml:lang="ru">Comptes Rendus. 1902. 10. Septembre.</mixed-citation>
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      <ref id="ref6">
        <label>6</label>
        <mixed-citation xml:lang="ru">Annali di Matematica t. 12. serie III.</mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>
