Ellipticity and Fredholmness of pseudo-differential operators on\n \ℓ²( Zn)

2019/10/12 by Aparajita Dasgupta, Vishvesh Kumar, Dasgupta, Aparajita +1
Computer Science · Mathematics · #35S05 #43A77 (Secondary) #43A85 #47G30 (Primary) #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1910.05582

openalex publication_date 2019/10/12 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

The minimal operator and the maximal operator of an elliptic\npseudo-differential operator with symbols on Zⁿ\× mathbbTⁿ are\nproved to coincide and the domain is given in terms of a Sobolev space.\nEllipticity and Fredholmness are proved to be equivalent for\npseudo-differential operators on Zⁿ. The index of an elliptic\npseudo-differential operator on Zⁿ is also computed.\n

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