Commuting differential operators of rank two

Hiroyuki Ochiai

doi:10.1016/0019-3577(96)85093-2

Commuting differential operators of rank two

Hiroyuki Ochiai

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Commuting differential operators with symbols ∂²₁ + ∂²₂, ∂²₁∂²₂ are related to the functional equation V₁(x₁)U₊(x₁ + x₂) + V₁(x₁)U_-(x₁ - x₂) + V₂(x₂)U₊(x₁ + x₂) - V₂(x₂)U_-(x₁ - x₂) = F_-(x₁ + x₂) + F_-(x₁ - x₂) + G₁(x₁) + G₂(x₂). We discuss several properties, such as a meromorphic extension of solutions and periodicity, of this functional equation and commuting differential operators.

Original language	English
Pages (from-to)	243-255
Number of pages	13
Journal	Indagationes Mathematicae
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/0019-3577(96)85093-2
Publication status	Published - Jun 17 1996
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/0019-3577(96)85093-2

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title = "Commuting differential operators of rank two",

abstract = "Commuting differential operators with symbols ∂21 + ∂22, ∂21∂22 are related to the functional equation V1(x1)U+(x1 + x2) + V1(x1)U-(x1 - x2) + V2(x2)U+(x1 + x2) - V2(x2)U-(x1 - x2) = F-(x1 + x2) + F-(x1 - x2) + G1(x1) + G2(x2). We discuss several properties, such as a meromorphic extension of solutions and periodicity, of this functional equation and commuting differential operators.",

author = "Hiroyuki Ochiai",

year = "1996",

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doi = "10.1016/0019-3577(96)85093-2",

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AU - Ochiai, Hiroyuki

PY - 1996/6/17

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N2 - Commuting differential operators with symbols ∂21 + ∂22, ∂21∂22 are related to the functional equation V1(x1)U+(x1 + x2) + V1(x1)U-(x1 - x2) + V2(x2)U+(x1 + x2) - V2(x2)U-(x1 - x2) = F-(x1 + x2) + F-(x1 - x2) + G1(x1) + G2(x2). We discuss several properties, such as a meromorphic extension of solutions and periodicity, of this functional equation and commuting differential operators.

AB - Commuting differential operators with symbols ∂21 + ∂22, ∂21∂22 are related to the functional equation V1(x1)U+(x1 + x2) + V1(x1)U-(x1 - x2) + V2(x2)U+(x1 + x2) - V2(x2)U-(x1 - x2) = F-(x1 + x2) + F-(x1 - x2) + G1(x1) + G2(x2). We discuss several properties, such as a meromorphic extension of solutions and periodicity, of this functional equation and commuting differential operators.

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Commuting differential operators of rank two

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