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Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable.
Walter Kurt Hayman, Patrick Brendan Kennedy,
1989
2
Growth Theory of
Subharmonic Functions
In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables.
3
Functions of One Complex Variable I
The first comment that should be made is that P is superharmonic iff — P is
subharmonic. Because of this, only the results on subharmonic functions will be
given and it will be left to the reader to state the analogous result for
superharmonic ...
4
Study of
Subharmonic Response in Nonlinear System Models
The report investigates the system model G(u, u dot, . . ., u sup n, t) = F(t), where F(t) is a periodic excitation.
Niles Ransom Moseley,
1971
5
Entire and
Subharmonic Functions
because u(z) = u(z) and for arg(z) = 0 we have the inequality 1 f^n 1 f^n u(r) = u(r)
^— u(r + pe'9)dy/ ^— u(r + pe'r)dy7. p < p(r). 2x J0 27t J0 If the function u(z) is
continuous and subharmonic in the annulus n, then, as was proved above, the ...
6
Function Theory of One Complex Variable
By the proposition, we conclude that (j) o f is subharmonic. The last example
raises a subtle point, which is worth making explicit. If / is harmonic and <j) is
convex, then (with only a small change) the argument we have just given shows
that 4> ...
Robert Everist Greene, Steven George Krantz,
2006
7
Introduction to Holomorphic Functions of Several Variables
There a number of equivalent characterizations of subharmonic functions, which
will be discussed in this and the next section. The particular characterization
chosen as the definition here is one of several commonly used as the definition
and ...
8
Introduction to Fourier Analysis on Euclidean Spaces
Before proceeding further in our brief study of subharmonic functions it will be
useful to present some examples: (1) It is clear that a harmonic function is
subharmonic. Moreover, it follows immediately from the definition that \u\ is
subharmonic ...
Elias M. Stein, Guido L. Weiss,
1971
9
Handbook of Complex Variables
7.7.6 The Maximum Principle A consequence of the sub-mean value property (
7.7.5.1) is the maximum principle for subharmonic functions: If / is subharmonic
on U and if there is a i3 £ [/ such that f(P) > f(z) for all z G U, then / is constant.
10
Classical Potential Theory
We have seen that harmonic functions on an open set Q can be characterized as
those finite- valued, continuous functions h on Q which satisfy the mean value
property: h(x) = M(h;x,r) whenever B(x,r) C Q. Subharmonic functions correspond
...
David H. Armitage, Stephen J. Gardiner,
2001
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «SUBHARMONIC»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
subharmonic w wiadomościach.
DigiTech Reissues the DOD Meatbox Subharmonic Bass Synthesizer
Salt Lake City, UT (July 6, 2015) -- For those who crave thick slabs of massive low end, HARMAN's DigiTech has put the legendary DOD Meatbox Subharmonic ... «Premier Guitar, Lip 15»
DOD revives Gonkulator Ring Modulator and Meatbox Subsynth …
The Meatbox, meanwhile, recreates the subharmonic synthesizing and low-end enhancement of the original, lending itself to use on bass, extended-range ... «MusicRadar.com, Lip 15»
More DOD Pedals Return
As a bass subharmonic synthesiSer and low-end enhancer, the Meatbox can produce a range of sounds from a slight thickening to a full-on, low-end assault! «Sonic State, Lip 15»
Ultrabroadband mid-IR frequency combs show promise for standoff …
Broadband (>1000nm) instantaneous outputs were reported in three setups: an erbium-fiber laser-pumped periodically poled lithium niobate subharmonic OPO ... «SPIE Newsroom, Mar 15»
[AES] Avid présente deux plug-ins Pro Series
La seconde nouveauté présentée par Avid est le Pro Subharmonic, un plug-in AAX Native/DSP 64 et AudioSuite 64 destiné à renforcer les basses de vos ... «Audiofanzine, Paz 14»
Sergei Tcherepnin creates works for the senses at MIT
The generic title “List Projects: Sergei Tcherepnin” does little to describe the installation, which has its own name: “Subharmonic Lick Thicket.” “Subharmonic” ... «Boston Globe, Lip 14»
Best of 2013: Popular music vs pundits
You will hear snatches of strange vocals, subharmonic frequencies and a high-hat that starts out innocently enough and then becomes an angry hiss. This is all ... «Mail & Guardian Online, Gru 13»
Device that can manipulate radiofrequency signals could soon …
The device, called a subharmonic passive mixer (see image), mixes an incoming millimeter wave that has a wavelength of 2.2 millimeters with a local source of ... «Phys.Org, Wrz 13»
SFist Interviews: Adam Theis Of Jazz Mafia
The line-up also included Subharmonic, a new brass-rock-groove band headed up by Adam Theis of the Jazz Mafia. Adam founded the Jazz Mafia collective, ... «SFist, Mar 13»
Jazz Mafia creator Adam Theis will bring new band Subharmonic to …
A one-man music industry in the Bay Area for 15 years, Theis -- who performs Saturday night at the San Jose Jazz Festival with Subharmonic, his new brass-led ... «San Jose Mercury News, Sie 12»