Analogs of generalized resolvents and eigenfunction expansions of relations generated by pair of differential operator expressions one of which depends on spectral parameter in nonlinear manner

2012/10/22 by Volodymyr Khrabustovskyi, Khrabustovskyi, Volodymyr · 2 citations
Computer Science · Mathematics · #34B05 #34B07 #34L10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CA #math.FA #math.SP #msc:34B05 #msc:34B07 #msc:34L10

paper · pdf · doi:10.48550/arxiv.1210.5988

arxiv created 2012/10/22 · openalex publication_date 2012/10/22 · arxiv updated 2012/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the relations generated by pair of differential operator expressions one of which depends on the spectral parameter in the Nevanlinna manner we construct analogs of the generalized resolvents which are integro-differential operators. The expansions in eigenfunctions of these relations are obtained.

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• Analogs of generalized resolvents of relations generated by pair of differential operator expressions one of which depends on spectral parameter in nonlinear manner
• Eigenfunction expansions associated with operator differential equation depending on spectral parameter nonlinearly

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