Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect

Yu. A. Ryabov

Displaying similar documents to “Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect”

Asymptotic relationship between solutions of two linear differential systems

Jozef Miklo (1998)

Mathematica Bohemica

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In this paper new generalized notions are defined: $Ψ$ -boundedness and $Ψ$ -asymptotic equivalence, where $Ψ$ is a complex continuous nonsingular $n \times n$ matrix. The $Ψ$ -asymptotic equivalence of linear differential systems $y^{'} = A (t) y$ and $x^{'} = A (t) x + B (t) x$ is proved when the fundamental matrix of $y^{'} = A (t) y$ is $Ψ$ -bounded.

Essential norms of a potential theoretic boundary integral operator in $L^{1}$

Josef Král, Dagmar Medková (1998)

Mathematica Bohemica

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Let $G \subset ℝ^{m}$ $(m \geq 2)$ be an open set with a compact boundary $B$ and let $σ \geq 0$ be a finite measure on $B$ . Consider the space $L^{1} (σ)$ of all $σ$ -integrable functions on $B$ and, for each $f \in L^{1} (σ)$ , denote by $f σ$ the signed measure on $B$ arising by multiplying $σ$ by $f$ in the usual way. $𝒩_{σ} f$ denotes the weak normal derivative (w.r. to $G$ ) of the Newtonian (in case $m > 2$ ) or the logarithmic (in case $n = 2$ ) potential of $f σ$ , correspondingly. Sharp geometric estimates are obtained for the essential norms of the operator $𝒩_{σ} - α I$ (here $α \in ℝ$ ...

Note on functions satisfying the integral Hölder condition

Josef, Jr. Král (1996)

Mathematica Bohemica

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Given a modulus of continuity $ω$ and $q \in [1, \infty [$ then $H_{q}^{ω}$ denotes the space of all functions $f$ with the period $1$ on $ℝ$ that are locally integrable in power $q$ and whose integral modulus of continuity of power $q$ (see(1)) is majorized by a multiple of $ω$ . The moduli of continuity $ω$ are characterized for which $H_{q}^{ω}$ contains “many” functions with infinite “essential” variation on an interval of length $1$ .

A method for determining constants in the linear combination of exponentials

Jiří Cerha (1996)

Mathematica Bohemica

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Shifting a numerically given function $b_{1} exp a_{1} t + \dots + b_{n} exp a_{n} t$ we obtain a fundamental matrix of the linear differential system $\dot{y} = A y$ with a constant matrix $A$ . Using the fundamental matrix we calculate $A$ , calculating the eigenvalues of $A$ we obtain $a_{1}, \dots, a_{n}$ and using the least square method we determine $b_{1}, \dots, b_{n}$ .

Displaying similar documents to “Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect”

Asymptotic relationship between solutions of two linear differential systems

Essential norms of a potential theoretic boundary integral operator in L 1

Note on functions satisfying the integral Hölder condition

A method for determining constants in the linear combination of exponentials

Essential norms of a potential theoretic boundary integral operator in $L^{1}$