Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients
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Publication:5632992
DOI10.1002/cpa.3160240505zbMath0226.35019OpenAlexW2062850071MaRDI QIDQ5632992
Publication date: 1971
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.3160240505
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Cites Work