Solutions of for rings

Author:
Burrell W. Helton

Journal:
Proc. Amer. Math. Soc. **25** (1970), 735-742

MSC:
Primary 45.10

DOI:
https://doi.org/10.1090/S0002-9939-1970-0259521-8

MathSciNet review:
0259521

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that there is a solution of the equation

**[1]**Burrell W. Helton,*Integral equations and product integrals*, Pacific J. Math.**16**(1966), 297–322. MR**0188731****[2]**Burrell W. Helton,*A product integral representation for a Gronwall inequality*, Proc. Amer. Math. Soc.**23**(1969), 493–500. MR**0248310**, https://doi.org/10.1090/S0002-9939-1969-0248310-8**[3]**J. V. Herod,*Multiplicative inverses of solutions for Volterra-Stieltjes integral equations*, Proc. Amer. Math. Soc.**22**(1969), 650-656.**[4]**J. S. MacNerney,*Integral equations and semigroups*, Illinois J. Math.**7**(1963), 148–173. MR**0144179****[5]**J. S. MacNerney,*A linear initial-value problem*, Bull. Amer. Math. Soc.**69**(1963), 314–329. MR**0146613**, https://doi.org/10.1090/S0002-9904-1963-10905-2

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0259521-8

Keywords:
Integral equations,
product integrals,
normed ring,
nonzero solutions,
linearly independent solutions,
divisors of zero,
bounded variation

Article copyright:
© Copyright 1970
American Mathematical Society