2019/12/08 by K. A. Mirzoev, Mirzoev, K. A., А. А. Шкаликов +2 · 2 citations
Mathematics · #34L99 #47E05 #Classical Analysis and ODEs (math.CA) #Combinatorics #Differential Equations and Boundary Problems #Differential operator #Distribution (mathematics) #FOS: Mathematics #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Order (exchange) #Physics #Spectral Theory in Mathematical Physics #math.CA #msc:34L99 #msc:47E05
paper · pdf · doi:10.48550/arxiv.1912.03660
6 pages, in Russian
openalex publication_date 2019/12/08 · arxiv created 2019/12/10 · arxiv updated 2019/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We work with differential expressions of the form τ2n+1 y =(-1)ni \(q0y(n+1))(n)+(q0y(n))(n+1)\+ ∑k=0n(-1)n+k(p(k)ky(n-k))(n-k)
+i∑k=1n(-1)n+k+1\(q(k)ky(n+1-k))(n-k)+ (q(k)ky(n-k))(n+1-k)\, where the complex valued coefficients pj and qj are subject the following conditions: q0(x) ∈ ACloc(a,b), Re q0>0, while all the other functions q1(x),q2(x),…,qn(x), p0(x),p1(x),…,pn(x) belong to the space L1loc(a,b). This implies that the coefficients p(k)k and q(k)k in the expression τ2n+1 are distributions of singularity order k. The main objective of the paper is to represent the differential expression τ2n+1 in the other (regularized) form which allows to define the minimal and maximal operators associated with this differential expression.