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Topic: Almost periodic function

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	PlanetMath: almost periodic function (classical definition)
		A function is called almost periodic iff set of its translates is pre-compact (compact after completion).
		The notion of an almost periodic function should not be confused with the notion of quasiperiodic function.
		This is version 10 of almost periodic function (classical definition), born on 2004-12-12, modified 2006-10-08.
	planetmath.org /encyclopedia/AlmostPeriodicFunction.html (436 words)

	PlanetMath: almost periodic function (equivalent definition)
		Not only is this definition simpler to state than that of Bohr, but it also generalizes to functions on groups.
		"almost periodic function (equivalent definition)" is owned by rspuzio.
		This is version 5 of almost periodic function (equivalent definition), born on 2005-07-10, modified 2006-10-10.
	planetmath.org /encyclopedia/AlmostPeriodicFunctionEquivalentDefinition.html (103 words)

	Almost periodic function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-02)
		In mathematics, almost periodicity is a property of dynamical systems that appear to retrace their paths through phase space, but not exactly.
		An example would be a planetary system, with planets in orbits moving with periods that are not commensurable (i.e., with a period vector that is not proportional to a vector of integers).
		This is the case for musical tones (after the initial attack transient) where all partials or overtones are harmonic (that is all overtones are at frequencies that are an integer multiple of a fundamental frequency of the tone).
	en.wikipedia.org /wiki/Almost_periodic_function (708 words)

	Periodic function - Wikipedia, the free encyclopedia
		Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period.
		The trigonometric functions sine and cosine are common periodic functions, with period 2π.
		an infinite image is given by the color as function of position, the periodicity of the function corresponds to translational symmetry of the object.
	en.wikipedia.org /wiki/Periodic_function (490 words)

	[No title]
		The effect on the >> >original function is to multiply it by a polynomial whose coeficients >> >are the same as those of the linear combination (except for factors of >> >i).
		In the periodic case specifying the period says something about how many frequencies there are in a given interval on the frequency side; the bound on the number of zeroes depends on this.
		If f is almost periodic and band-limited then it can gave only finitely many zeroes in a bounded interval, but to get a bound on how many I think you're going to need to specify something analogous to specifying the period in the periodic case.
	www.math.niu.edu /~rusin/known-math/00_incoming/band_lim (3877 words)

	OhioLINK ETD: Alsulami, Saud
		As a tool to investigate almost periodic functions of several variables which is important for the study of asymptotic behavior of Eq.(), we give answer to a question raised by Basit in 1971, which is an extension of the classical Bohl-Bohr theorem (to almost* periodic functions with two or more variables).
		As an application, we obtain a result on the almost periodicity of a double integral of an almost periodic function defined on the plane.
		For the infinite dimensional case, and under the conditions that A and B are bounded linear operators, we reduce the question of the almost periodicity (resp, almost automorphicity) of the differential equations () for given almost* periodic (resp, almost automorphic) functions f
	www.ohiolink.edu /etd/view.cgi?ohiou1126042587 (398 words)

	No title
		Classically, the class of almost periodic functions is closed under addition and multiplication, but constructively this is not the case.
		It is, however, straightforward to prove that the almost periodic functions are closed under uniform limits.
		On the almost periodicity of trigonometric polynomials in constructive mathematics.
	www.cs.ru.nl /~spitters/almostper.html (2719 words)

	Springer Online Reference Works
		The theory of almost-periodic functions was initiated by H.
		As to the equivalence of the approach starting from a certain structural property that is a generalization of pure periodicity, and on the other hand, the approach starting from approximation by trigonometric polynomials (also in the definition of the various classes of generalized almost-periodic functions), see [2], Chapt.
		A new approach to the theory of uniformly almost-periodic functions is given in [a1]; this has lead to the study of so-called almost-automorphic functions [a9], a class of functions closely related to the Levitan almost-periodic functions mentioned above [a7].
	eom.springer.de /A/a011970.htm (994 words)

	Colloq. Talk Oct. 17, 2000 (Site not responding. Last check: 2007-11-02)
		An almost periodic function is the generalization of the idea of a periodic function.
		The properties of almost periodic functions on other domains appear to be less well known.
		Attempts to apply the same variational schemes to the analogous elliptic partial differential equations may fail because of the essential differences between almost periodic functions of one variable and of several variables.
	www.math.fau.edu /HTMLFILE/EVENTS/co01017.html (143 words)

	Springer Online Reference Works
		A class of almost-periodic functions in which the analogue of the Riesz–Fischer theorem is valid: Any trigonometric series
		The definition of these functions [1], [2] is based on a generalization of the concept of an almost-period, and certain additional ideas must be introduced in it.
		is a real-valued function, defined, respectively, for a real variable and an integer argument.
	eom.springer.de /b/b015820.htm (243 words)

	Almost periodic particle dynamics in the Vlasov limit
		In this section almost periodicity appears in a different way, particles no longer move on a discrete grid as before but as a gas in
		As in the case of almost periodic CA, there are macroscopic quantities which are invariant under the Vlasov flow.
		is a measure for the growth rate of complexity of the almost periodic fluid.
	www.math.harvard.edu /~knill/oldinterests/complexity/node3.html (723 words)

	T. Tonev - Big Disc etc. (Book) (Site not responding. Last check: 2007-11-02)
		A picture of the latest developments in analytic almost periodic function theory in a contemporary uniform algebra setting is given in Chapter II.
		Analytic Gamma-almost-periodic functions in domains of the complex plane are presented as Gamma-analytic functions in corresponding domains of the big-plane.
		Properties of Gamma-analytic functions defined on arbitrary subsets in the big-plane and in particular in the big-disc are presented in Sections 2.4 and 2.6.
	lennes.math.umt.edu /~tonev/bdisc.html (734 words)

	Category:Complex analysis - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		functions which are defined in some region of the complex plane, take complex values, and are differentiable as complex functions.
		For instance, every holomorphic function is representable as power series in every open disc in its domain of definition, and is therefore analytic.
		Most elementary functions, such as all polynomials, the exponential function, and the trigonometric functions, are holomorphic.
	en.wikipedia.org.cob-web.org:8888 /wiki/Category:Complex_analysis (184 words)

	CMFT 1 (2001), 403--415 (Site not responding. Last check: 2007-11-02)
		We extend the notion of amoeba to holomorphic almost periodic functions in tube domains.
		In this setting, the order of a function in a connected component of the complement of its amoeba is just the mean motion of this function.
		Almost periodic function, amoeba, zero set, mean motion, exponential sum.
	www.heldermann.de /CMF/CMF01/cmf0127.htm (96 words)

	Periodic Function -- from Wolfram MathWorld (via CobWeb/3.1 planetlab1.isi.jhu.edu) (Site not responding. Last check: 2007-11-02)
		is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period
		The following table summarizes the names given to periodic functions based on the number of independent periods they posses.
		Periodic Point, Periodic Sequence, Singly Periodic Function, Triply Periodic Function.
	mathworld.wolfram.com.cob-web.org:8888 /PeriodicFunction.html (159 words)

	T. Tonev - PUBLICATIONS(Reviewed in the Math Reviews)
		Function spaces (Edwardsville, IL, 1990), 405--412, Lecture Notes in Pure and Appl.
		Functional analytic methods in complex analysis and applications to partial differential equations (Trieste, 1988), 265--286, World Sci.
		Analytic functions, B\l a\.zejewko 1982 (B\l a\.zejewko, 1982), 436--442, Lecture Notes in Math., 1039, Springer, Berlin, 1983.
	www.math.umt.edu /tonev/list03.html (1283 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		We show that $R(E)$ is of the form $E^{(d-1)/2}\,\Theta(\sqrt{E})$, where $\Theta(x)$ is an almost periodic function of Besicovitch class $B^2$ which has a limit distribution whose density is a box-shaped function.
		Furthermore we derive a trace formula and study higher order terms in the asymptotics of the coefficients related to the periodic orbits.
		The periodicity of the geodesic flow leads to a very simple structure of the trace formula which is the reason why the limit distribution can be computed explicitly.
	www.ma.utexas.edu /mp_arc/abstracts/95-220 (154 words)

	Springer Online Reference Works
		A branch of functional analysis in which one studies the behaviour on the real axis
		or weak almost-periodicity (that is, almost periodicity of the scalar functions
		For almost-periodic solutions the specifics of an infinite-dimensional space are already encountered in a generalization of the well-known Bohl–Bohr theorem on the almost-periodicity of a bounded integral of an almost-periodic function, that is, on the almost-periodicity of a solution of the simplest differential equation
	eom.springer.de /q/q076250.htm (1687 words)

	Atlas: Solution to Some Singular Integro-Differential Equations in the Space of Semi-Almost Periodic Distributions by ...
		Let a(t) be an infinitely differentiable almost periodic function in the sense of Bohr and f be a semi-almost periodic distribution defined on the real line and let H be the operator of Hilbert transform defined on these spaces.
		The space of semi-almost periodic distribution that we choose contains the Schwartz space of almost periodic distributions as well as regular distributions generated by the space of simple functions defined on the real line.
		We have also considered the generalisations of these problems when a(t) is an n × n matrix whose elements are infinitely differentiable almost periodic functions on R and f is an n-column vector with almost periodic or semi-almost periodic elements.
	atlas-conferences.com /cgi-bin/abstract/cakr-34 (272 words)

	Rodman's talk (Site not responding. Last check: 2007-11-02)
		Almost periodic factorization of A(t) has the form
		The theory of almost periodic factorization is being developed recently, motivated by applications such as convolution equations on finite intervals.
		A review of the existing factorization theory of almost periodic matrix functions will be given.
	www.cs.bgu.ac.il /~barakw/colloquium/rodman/rodmanabs (124 words)

	OUP: UK General Catalogue
		Almost periodic numeric sequences and their connection with almost periodic functions
		The behavior at infinity of analytic almost periodic functions in a half-plane
		The Fourier series attached to an almost periodic function with values in a Banach space.
	www.oup.com /uk/catalogue/?ci=9780828403313 (239 words)

	Almost Periodic Function (Site not responding. Last check: 2007-11-02)
		almost periodic function (equivalent definition) (Definition) There is an equivalent definition of almost periodic function due to Bochner:
		Almost periodic function Free Bored Net Online Encyclopedia resource..
		Almost periodic function,brain function,corporate entertainment,ebay survey.taf function nextq,function of management,function of pancreas,function
	www.almostperiodicfunction.info (250 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		The first one is the topological group G of all orientation-preserving selfhomeomorphisms of the closed interval.
		We show that every weakly almost periodic function on G is constant (conjectured by V. Pestov).
		This implies that every semitopological semigroup compactification of it is trivial (answering a question of W. Ruppert) and every weakly continuous REFLEXIVE representation of G is trivial.
	www.math.technion.ac.il /~techm/20020512120020020512meg (147 words)

	Bohr, Harald August (1887-1951) -- from Eric Weisstein's World of Scientific Biography
		Later, he concentrated his efforts on a study of the Riemann zeta function
		In 1914, Landau and Bohr formulated a theorem concerning the distribution of zeros of the zeta function (now called the Bohr-Landau theorem).
		In three papers published in 1924-26 in Acta Mathematica, Bohr founded the theory of almost periodic function.
	scienceworld.wolfram.com /biography/BohrHarald.html (172 words)

	NSDL Metadata Record -- Almost Periodic Function -- from MathWorld
		NSDL Metadata Record -- Almost Periodic Function -- from MathWorld
		A function representable as a generalized Fourier series.
		Following Bohr (1947), a continuous function x(t) for (-\infty
	nsdl.org /mr/698040 (108 words)

	Stepanov (print-only) (Site not responding. Last check: 2007-11-02)
		He returned to Moscow and, much influenced by Egorov and Luzin, he worked on periodic functions and differential equations.
		He was appointed Director of the Research Institute of Mathematics and Mechanics from 1939, a post he held until his death.
		Harald Bohr had introduced the notion of an almost periodic function and Stepanov constructed and investigated new classes of these functions.
	www-groups.dcs.st-and.ac.uk /~history/Printonly/Stepanov.html (140 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		From: israel@math.ubc.ca (Robert Israel) Subject: Re: almost periodic function Date: 26 Apr 2001 20:17:44 GMT Newsgroups: sci.math In article
		A function on a locally compact abelian group is almost periodic if it is a uniform limit of trigonometric polynomials.
		One reason they might be interesting for physics is that under certain conditions, stable solutions of almost periodic differential equations are almost periodic.
	www.math.niu.edu /~rusin/known-math/01_incoming/almost_period (103 words)

	MATHEMATICA BOHEMICA, Vol. 124, No. 4, pp. 351-379, 1999 (Site not responding. Last check: 2007-11-02)
		Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag
		Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.
		Keywords: almost periodic function, Fourier coefficient, Fourier exponent, spectrum of almost periodic function, almost periodic system of differential equations, formal almost periodic solution, almost periodic solution, distance of two spectra, time lag
	www.emis.de /journals/MB/124.4/2.html (132 words)

	[No title]
		Finally, we deduce that every graph that can arise as the principal graph of a finite depth subfactor of index 4 actually arises for one arising from a vertex model corresponding to B(2, n) for some n.
		Transformation semigroup compactifications and norm continuity of weakly almost periodic functions
		We prove if there exists a separately continuous action of a topologically right simple semitopological semigroup S on a topologoical space X and if S acts topologically surjective on X then each weakly almost periodic function on X, with respect to S, is left norm continuous.
	www.ias.ac.in /mathsci/vol110/feb2000/absfeb2000.html (608 words)

	periodic - OneLook Dictionary Search
		PERIODIC : Navajo Code Talkers' Dictionary [home, info]
		Periodic : The Computational Beauty of Nature [home, info]
		Phrases that include periodic: periodic table, periodic law, periodic motion, periodic breathing, almost periodic function, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=periodic (248 words)

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