Linear ordinary differential equations with constant coefficients over a Banach algebra (Q2518053)
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| Language | Label | Description | Also known as |
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| English | Linear ordinary differential equations with constant coefficients over a Banach algebra |
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Linear ordinary differential equations with constant coefficients over a Banach algebra (English)
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12 January 2009
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The left-side linear differential equation \[ \sum_{n=0}^N A_n\dfrac{d^{N-n}X}{dt^n}=0, \tag{1} \] with constant coefficients \(A_n\) over a noncommutative Banach algebra is considered. Sufficient conditions are obtained to present the solutions of (1) in the Euler form, i.e. as the sum of the products of exponential functions, polynomials, and trigonometric functions (sines and cosines).
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left-side linear differential equation
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Banach algebra
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solution of the Euler type
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