Measure of the level set for solutions of ordinary differential equations with constant coefficients(in Ukrainian) |
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Author |
ilkivv@i.ua
Lviv Polytechnic National University,
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
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Abstract |
For a real functions
f∈Cn[a,b]
such that
|Lnf(x)|≥δ
on
[a,b],
where
Ln
is a differential expression, namely
Ln=(d/dx+λ1)⋯(d/dx+λn)
with real
λ1,…,λn,
we find a Lebesgue measure
estimate for the level set
GLn(ε,δ;f)={x∈[a,b]:|f(x)|≤ε}.
In particular, we establish the inequality
measGLn(ε,δ;f)≤min
where
q_n=\prod_{r=1}^n \frac{|\lambda_r|(b-a)/2}{\mathop{\rm th}|\lambda_r|(b-a)/2}.
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Keywords |
Lebesgue measure; level sets; small denominators
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Reference |
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Pages |
146-156
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Volume |
41
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Issue |
2
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Year |
2014
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Journal |
Matematychni Studii
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Full text of paper | |
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