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    <Journal>
      <PublisherName>ijesm</PublisherName>
      <JournalTitle>International Journal of Engineering, Science and</JournalTitle>
      <PISSN>I</PISSN>
      <EISSN>S</EISSN>
      <Volume-Issue>volume 15,issue 8</Volume-Issue>
      <PartNumber/>
      <IssueTopic>Multidisciplinary</IssueTopic>
      <IssueLanguage>English</IssueLanguage>
      <Season>August 2026</Season>
      <SpecialIssue>N</SpecialIssue>
      <SupplementaryIssue>N</SupplementaryIssue>
      <IssueOA>Y</IssueOA>
      <PubDate>
        <Year>-0001</Year>
        <Month>11</Month>
        <Day>30</Day>
      </PubDate>
      <ArticleType>Engineering, Science and Mathematics</ArticleType>
      <ArticleTitle>STUDY OF CHARACTERIZATION OF SPECTRAL MEASURES ON BANACH SPACE AND ITS IMPACT</ArticleTitle>
      <SubTitle/>
      <ArticleLanguage>English</ArticleLanguage>
      <ArticleOA>Y</ArticleOA>
      <FirstPage>35</FirstPage>
      <LastPage>43</LastPage>
      <AuthorList>
        <Author>
          <FirstName>ANISH KUMAR and Dr. Mukund Kumar</FirstName>
          <LastName>Singh</LastName>
          <AuthorLanguage>English</AuthorLanguage>
          <Affiliation/>
          <CorrespondingAuthor>N</CorrespondingAuthor>
          <ORCID/>
        </Author>
      </AuthorList>
      <DOI/>
      <Abstract>We derive some properties of co-relation operator and its spectral measure. We derive theorems related to Lebesque decomposition theorem and Hellinger integrals. The stationary sequence play a crucial role in determining spectral measure and angle between the part and future of a stationary sequence.  we derive here the characteristic properties of the spectral measures on stochastic processes and its regularity condition. We discuss characteristic properties of the regularized version of a stochastic process equivalent to the modified application of random variables and its application to Ito__ampersandsignrsquo;s construction of simple paths of a given process. The significant aspect in Ito__ampersandsigncent;s construction consists of the regularization of the sample paths of the given process.</Abstract>
      <AbstractLanguage>English</AbstractLanguage>
      <Keywords/>
      <URLs>
        <Abstract>https://www.ijesm.co.in/ubijournal-v1copy/journals/abstract.php?article_id=16347&amp;title=STUDY OF CHARACTERIZATION OF SPECTRAL MEASURES ON BANACH SPACE AND ITS IMPACT</Abstract>
      </URLs>
      <References>
        <ReferencesarticleTitle>References</ReferencesarticleTitle>
        <ReferencesfirstPage>16</ReferencesfirstPage>
        <ReferenceslastPage>19</ReferenceslastPage>
        <References/>
      </References>
    </Journal>
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