Results 271 to 280 of about 9,396 (291)

Range of the Radon Transform on Functions which Do No Decay Fast at Infinity

SIAM Journal on Mathematical Analysis, 1997
Summary: Let an integer \(m\geq0\) be fixed. Let \({\mathcal X}_m\) be the space of functions \(f\in C^\infty(\mathbb{R}^n)\) that admit an asymptotic expansion \(f(r\beta)\sim\sum_{k=m}^\infty\psi_k(\beta)/r^{n+k}\), \(r\to\infty\), \(\psi_k\in C^\infty(S^{n-1})\), and the expansion can be differentiated with respect to \(x=r\beta\) any number of ...
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Functions Whose Fourier Transforms Decay at Infinity: An Extension of the Riemann-Lebesgue Lemma

SIAM Journal on Mathematical Analysis, 1972
An extension of the Riemann–Lebesgue lemma is stated and proved. We define the space $LL$ of all complex-valued locally integrable functions on $[0, + \infty )$, and the space $RL$ of all functions...
Bleistein, Norman, Handelsman, Richard A., Lew, John S.   +2 more
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On Linear Perturbations Decaying at Infinity and Altering the Lyapunov Exponents of Regular Linear Differential Systems

Differential Equations, 2021
In this paper, the author addresses a classical problem on the instability of Lyapunov exponents, \(\lambda_i(A)\), \(i=1,2,\cdots,n\) of linear system of ordinary differential equations \[ \dot x = A(t) x, \quad t\ge 0, \ x\in {\mathbb R}^n.\tag{S} \] The main result states that for any positive, monotone increasing function \(\theta(t)\) such that \(\
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Heat kernel estimates for Schrödinger operators with decay at infinity on parabolic manifolds

Transactions of the American Mathematical Society
We give estimates for positive solutions for the Schrödinger equation $(Δ_μ+W)u=0$ on a wide class of parabolic weighted manifolds $(M, dμ)$ when $W$ decays to zero at infinity faster than quadratically. These can be combined with results of Grigor'yan to give matching upper and lower bounds for the heat kernel of the corresponding Schrödinger operator
Graves-McCleary, Anthony, Saloff-Coste, Laurent   +1 more
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On Solutions Decaying at Infinity of Real Nonautonomous Systems of Quasilinear Differential Equations

Differential Equations, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Examples of GES Systems That can be Driven to Infinity by Arbitrarily Small Additive Decaying Exponentials

IEEE Transactions on Automatic Control, 2004
Examples are given of nonlinear, time-invariant systems in continuous-time, discrete-time, and of hybrid type, that have linear sector growth, the origin globally exponentially stable, and that can be driven to infinity by arbitrarily small additive decaying exponentials.
Andrew R. Teel, João Pedro Hespanha
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Bounds on the number of bound states for potentials with critical decay at infinity

Journal of Mathematical Physics, 1990
Let V be a potential whose negative part V− decays like c‖x‖−2 at infinity. If c is not too large, then the Schrödinger operator HV=−Δ+V on Rn, n≥3, has only a finite number of bound states although the associated classical phase space volume is infinite. Optimal conditions are derived for the absence of bound states and a family of bounds on the total
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Uniqueness for Cauchy problems for parabolic equations with rapid decay at infinity

Journal of Inverse and Ill-posed Problems
Abstract In this paper, we proved two types of uniqueness results for solutions to parabolic equations whose traces at time T > 0
Oleg Imanuvilov, Masahiro Yamamoto
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Functions Whose Fourier Transforms Decay at Infinity: Qualitative Criteria for an Additional Case

SIAM Journal on Mathematical Analysis, 1974
A previous paper of Bleistein, Handelsman and Lew describes the asymptotic behavior of \[F(\omega ) = \mathop {\lim }\limits_{u \to + \infty } \int_0^u {\exp (i\omega t)f(t)dt} \]for certain functions f on $[0, + \infty )$. It estimates the growth or decay of F near $ + \infty $ when f has a suitable asymptotic expansion, then establishes the decay in ...
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Gaussian decay for the eigenfunctions of a schrödinger operator with magnetic field constant at infinity

Communications in Partial Differential Equations, 1998
(1998). Gaussian decay for the eigenfunctions of a schrodinger operator with magnetic field constant at infinity. Communications in Partial Differential Equations: Vol. 23, No. 1-2, pp. 247-274.
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