Algebraic Aspects in the Theory of Systems of Linear Differential Equations
Algebraic Aspects in the Theory of Systems of Linear Differential Equations
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In our eReader you can find the full English version of the book. Read Algebraic Aspects in the Theory of Systems of Linear Differential Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Algebraic Aspects in the Theory of Systems of Linear Differential Equations
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To quickly assess the difficulty of the text, read a short excerpt:
- p^ [pMl - 0.
Since p ^ 0, combining (22) and (2U) we find that C « 0, and this finishes the proof of the first part of Theorem IV.
The statement in Theorera IV about (lU) being a sufficient condition for (13) to be true is almost trivial. To show that it is not a necessary condition we take n » 1 and (°x 'y°- A(t) « (cost - cos2t ) I )for 2n .
(t-2n)5' Clearly > t (26) IMt), / A(s)ds 1 - 'o but if 2ti, then (27) [a(s^), A(e2) J ¥ 0.
It remains an open question whether (lU) is a necessary co...ndition for the vanishing of all Lie-integral functionals of weight m > n if A(t) can be expanded in a power series in t.
- 28 - VI. Conditions for the Existence of a Solution Y « exp-TI for Y - AY» Ve consider again a system of linear differential equations of the first order: (1) § - A(t) T(t), where Y and A are n by n matrices the elements of which are functiohs of a para- meter t. We assume again that Y(o) is the identity I and that A(t) is continu- ous in t, although it is well known that the latter condition could be weakened.
What to read after Algebraic Aspects in the Theory of Systems of Linear Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
- p^ [pMl - 0.
Since p ^ 0, combining (22) and (2U) we find that C « 0, and this finishes the proof of the first part of Theorem IV.
The statement in Theorera IV about (lU) being a sufficient condition for (13) to be true is almost trivial. To show that it is not a necessary condition we take n » 1 and (°x 'y°- A(t) « (cost - cos2t ) I )for 2n .
(t-2n)5' Clearly > t (26) IMt), / A(s)ds 1 - 'o but if 2ti, then (27) [a(s^), A(e2) J ¥ 0.
It remains an open question whether (lU) is a necessary co...ndition for the vanishing of all Lie-integral functionals of weight m > n if A(t) can be expanded in a power series in t.
- 28 - VI. Conditions for the Existence of a Solution Y « exp-TI for Y - AY» Ve consider again a system of linear differential equations of the first order: (1) § - A(t) T(t), where Y and A are n by n matrices the elements of which are functiohs of a para- meter t. We assume again that Y(o) is the identity I and that A(t) is continu- ous in t, although it is well known that the latter condition could be weakened.
What to read after Algebraic Aspects in the Theory of Systems of Linear Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read onlineMoreLess
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