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Topic: Hilbert

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Hilbert space

David Hilbert

Hilbert transform

Reproducing kernel Hilbert space

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Hilbert Schenck

Rigged Hilbert space

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	David Hilbert - Wikipedia, the free encyclopedia
		David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries.
		Hilbert's basis theorem solved the principal problem in nineteenth century invariant theory by showing that any form of a given number of variables and of a given degree has a finite, yet complete system of independent rational integral invariants and covariants.
		Hilbert helped provide the basis for the theory of automata which was later built upon by computer scientist Alan Turing.
	en.wikipedia.org /wiki/David_Hilbert (844 words)

	Hilbert space - Wikipedia, the free encyclopedia
		Hilbert spaces serve to clarify and generalize the concept of Fourier expansion and certain linear transformations such as the Fourier transform.
		Hilbert spaces are of crucial importance in the mathematical formulation of quantum mechanics, although many basic features of quantum mechanics can be understood without going into details about Hilbert spaces.
		Hilbert spaces were named after David Hilbert, who studied them in the context of integral equations.
	en.wikipedia.org /wiki/Hilbert_space (1813 words)

	David Hilbert: Tutte le informazioni su David Hilbert su Encyclopedia.it
		David Hilbert, nato il 23 gennaio 1862 a Königsberg, Prussia (l'odierna Kaliningrad, Russia) e morto il 14 febbraio 1943 a Göttingen, Germania, è stato uno dei più eminenti matematici a cavallo tra il XIX e il XX secolo.
		Hilbert rimase all'Università come docente dal 1886 al 1895, quando in seguito all'interessamento di Klein ottenne la cattedra di Matematica a Göttingen, dove restò fino alla fine della sua carriera.
		L'articolo di Hilbert uscì il 6 dicembre senza le equazioni, quello di Einstein il 2.
	www.encyclopedia.it /d/da/david_hilbert.html (1046 words)

	Hilbert Space
		Hilbert space is not a space of simple points, rather it is a space of functions at a higher level of mathematical abstraction.
		Rather, Hilbert space is a mathematical device for arranging pieces of information, with each complex coordinate representing a possibility, or probability amplitude, for a given quantum state that might correspond to a definite eigenvalue for energy, or position, or momentum, or spin, etc. Note, that not all of these observable properties can be definite simultaneously.
		Although the total quantum state is a ray in which only the direction in Hilbert space is physically observable, the projective coordinates of this ray, onto a frame of reference of basic rays, are two-real dimensional vectors in the complex plane in which both the magnitude and relative direction are important.
	www.qedcorp.com /pcr/pcr/hilberts.html (2670 words)

	Hilbert
		Hilbert was a member of staff at Königsberg from 1886 to 1895, being a Privatdozent until 1892, then as Extraordinary Professor for one year before being appointed a full professor in 1893.
		Hilbert's eminent position in the world of mathematics after 1900 meant that other institutions would have liked to tempt him to leave Göttingen and, in 1902, the University of Berlin offered Hilbert Fuchs' chair.
		Hilbert himself tried at first to follow Gordan's approach but soon realised that a new line of attack was necessary.
	www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Hilbert.html (1570 words)

	Hilbert's program - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-21)
		Hilbert's Program was to formalize all existing theories to finite 'real' complete set of axioms, and provide a proof that these axioms were consistent.
		Hilbert's Program was proposed by German mathematician David Hilbert in 1920.
		Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems.
	encyclopedia.worldsearch.com /hilbert%27s_program.htm (178 words)

	The Seattle Times: Seattle History
		Hilbert is an Upper Skagit elder who has spent the bulk of her adult life researching, documenting and translating the ways and words of Lushootseed — the culture and language of Puget Sound's indigenous people.
		But the elders Hilbert interviewed, the last of the Lushootseed speakers to remember the stories and ceremonies handed down from their elders, were grateful someone wanted to know what they knew of the old ways.
		Hilbert was in her early 40s with a husband and two nearly grown children when she met Thom Hess, a UW linguistics grad student in 1967.
	seattletimes.nwsource.com /news/local/seattle_history/articles/hilbert.html (1490 words)

	David Hilbert (Site not responding. Last check: 2007-10-21)
		In 1895, Hilbert was appointed to the chair of mathematics at the University of Göttingen, where he continued to teach for the rest of his career.
		Hilbert submitted a paper on the subject, and despite objections from Gordan, the world expert on invariant theory, it was accepted.
		Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations.
	www.stetson.edu /~efriedma/periodictable/html/H.html (516 words)

	Hilbert's Program
		He argues that whereas the intuition involved in Hilbert's early papers was a kind of perceptual intuition, in later writings (e.g., Bernays 1928a) it is identified as a form of pure intuition in the Kantian sense.
		Hilbert never gave a general account of which operations and methods of proof are acceptable from the finitist standpoint, but only examples of operations and methods of inference in contentual finitary number theory which he accepted as finitary.
		Although Hilbert's first proposals focused exclusively on consistency, there is a noticeable development in Hilbert's thinking in the direction of a general reductivist project of a sort quite common in the philosophy of science at the time (as was pointed out by Giaquinto 1983).
	plato.stanford.edu /entries/hilbert-program (7534 words)

	DAVID HILBERT (Site not responding. Last check: 2007-10-21)
		For many years, Hilbert held the position at the Mathematical Institute at the University of Göttingen that was recognized as the most prestigious mathematical position in Germany, and possibly, in the world.
		After all, the Senate is not a bathhouse." Noether's application was rejected, but Hilbert arranged for her to stay at Göttingen by having her lectures announced under his name.
		Hilbert's scientific activity can be roughly divided into six periods, according to the years of publication of the results: up to 1893 (at Königsberg), algebraic forms; 1894-1899, algebraic number theory; 1899-1903, foundations of geometry; 1904-1909, analysis (Dirichlet's principle, calculus of variations, integral equations, Waring's problem); 1912-1914, theoretical physics; after 1918, foundations of mathematics.
	faculty.evansville.edu /ck6/bstud/hilbert.html (511 words)

	Hilbert's basis theorem (Site not responding. Last check: 2007-10-21)
		In mathematics, Hilbert's basis theorem, first proved by David Hilbert in 1888, states that, if ''k is a field, then every ideal in the ring of multivariate polynomials k''[''x
		Hilbert produced an innovative proof by contradiction using mathematical induction ; his method does not give an algorithm to produce the finitely many basis polynomials for a given ideal: it only shows that they must exist.
		A slightly more general statement of Hilbert's basis theorem is: if R is a left (respectively right) Noetherian ring, then the polynomial ring R''[''X''] is also left (respectively right) Noetherian.
	www.serebella.com /encyclopedia/article-Hilbert's_basis_theorem.html (207 words)

	PlanetMath: Hilbert space
		In particular, a Hilbert space is a Banach space in the norm induced by the inner product, since the norm and the inner product both induce the same metric.
		Any finite-dimensional inner product space is a Hilbert space, but it is worth mentioning that some authors require the space to be infinite dimensional for it to be called a Hilbert space.
		This is version 8 of Hilbert space, born on 2002-02-13, modified 2004-12-07.
	planetmath.org /encyclopedia/HilbertSpace.html (168 words)

	Hilbert College (Site not responding. Last check: 2007-10-21)
		John Manth, adjunct instructor of criminal justice at Hilbert College in Hamburg, New York, points to the increasing number of issues kids are dealing with at...
		Hilbert stays on the court to face the...
		Hilbert College is currrently a four-year co-education college.
	www.wikiverse.org /hilbert-college (190 words)

	What (Hilbert Curve) (Site not responding. Last check: 2007-10-21)
		The Hilbert Curve was studied by David Hilbert at the turn of the century as an example 1-dimensional curve filling a 2-dimensional space.
		The Hilbert Curve is one of the earliest "curious curves" known to have been studied.
		Hilbert and Peano were interested in such curves at the end of the 19th century.
	www.shodor.org /interactivate/activities/hilbert1/what.html (184 words)

	The Epsilon Calculus
		Hilbert's range of mathematical interests was broad, and included an interest in the foundations of mathematics: his Foundations of Geometry was published in 1899, and of the list of questions posed to the International Congress of Mathematicians in 1900, three addressed distinctly foundational issues.
		Although Hilbert was impressed by the work of Russell and Whitehead in their Principia Mathematica, he became convinced that the logicist attempt to reduce mathematics to logic could not succeed, due in particular to the non-logical character of their axiom of reducibility.
		Hilbert's lectures from 1917-1918 already note that one can easily prove the consistency of propositional logic, by taking propositional variables and formulae to range over truth values 0 and 1, and interpreting the logical connectives as the corresponding arithmetic operations.
	plato.stanford.edu /entries/epsilon-calculus (6438 words)

	Mathematical Problems of David Hilbert (Site not responding. Last check: 2007-10-21)
		Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics.
		In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century.
		Although almost a century old, Hilbert's address is still important and should be read (at least in part) by anyone interested in pursuing research in mathematics.
	aleph0.clarku.edu /~djoyce/hilbert (363 words)

	A Precise Explication of Hilbert's Program
		Hilbert's description of the ``big system,'' corresponding to infinitistic mathematics, is already sufficiently precise.
		Hilbert's plan was to carry out a consistency proof which would be obviously finitistic.
		Hilbert's plan to reduce all of mathematics to finitism is only one of many possible reductionist schemes.
	www.math.psu.edu /simpson/papers/hilbert/node3.html (736 words)

	The Hilbert curve
		The Hilbert curve is a space filling curve that visits every point in a square grid with a size of 2×2, 4×4, 8×8, 16×16, or any other power of 2.
		The Hilbert curve is also a special version of a quadtree; any image processing function that benefits from the use of quadtrees may also use a Hilbert curve.
		The second order Hilbert curve replaces that cup by four (smaller) cups, which are linked together by three joins (see the figure on the right; the link between a cup and a join has been marked with a fat dot in the figure).
	www.compuphase.com /hilbert.htm (544 words)

	Hilbert's Statement of His Program
		Hilbert accepts the picture of the world which is presented by contemporary physics.
		Hilbert concludes that the mathematician's infinity does not correspond to anything in the physical world.
		Hilbert viewed this as a new manifestation of the method of ideal elements.
	www.math.psu.edu /simpson/papers/hilbert/node2.html (856 words)

	hilbert
		Hilbert's inequalities are usually presented as a pair of statements applying to sequences
		This short and elegant method is in fact a refinement of Hilbert's original proof.
		The right-hand inequality is a strengthening of Hilbert's inequality, and the left-hand one represents new information.
	www.maths.lancs.ac.uk /~jameson/hilbert (805 words)

	David Hilbert
		David Hilbert was born in Koenigsberg, East Prussia in 1862 and received his doctorate from his home town university in 1885.
		Hilbert's axioms could be proved as theorems from Moore's and conversely, Moore's axioms could be proved as theorems from Hilbert's.
		Sometimes a mimeographed copy of the the paper would circulate before the actual publication and you would try to get your hands on a copy of it as quickly as possible, especially if you, yourself, had been working on the problem and had been leaning toward a result that was contrary to the current rumor.
	www.sonoma.edu /Math/faculty/falbo/hilbert.html (1070 words)

	Hilbert, David (Site not responding. Last check: 2007-10-21)
		After making a systematic study of the axioms of Euclidean geometry, Hilbert proposed a set of 21 such axioms and analyzed their significance.
		Hilbert received his Ph.D. from the University of Konigsberg and served on its faculty from 1886 to 1895.
		Hilbert contributed to several branches of mathematics, including algebraic number theory, functional analysis, mathematical physics, and the calculus of variations.
	euler.ciens.ucv.ve /English/mathematics/hilbert.html (153 words)

	Hilbert Space Explorer Home Page
		Hilbert space [external] underlies the foundation of quantum mechanics, and there is a strong physical and philosophical motivation to understand its properties.
		A practical problem with this approach is that the direct definition of a Hilbert space is large and awkward to work with, unless we already have available an underlying theory of vector spaces, etc. (which at this point I do not have).
		The set of closed subspaces of Hilbert space obey the laws of a simple equational algebra called "orthomodular lattice algebra." This algebra is sometimes called "quantum logic," and it can be used as the basis for a propositional calculus that resembles but is somewhat weaker than standard (classical) propositional calculus.
	us.metamath.org /mpegif/mmhil.html (2104 words)

	Hilbert C*-Modules Home Page
		Hilbert C*-modules are an often used tool in operator theory and in operator algebra theory.
		At the contrary, the pieces of Hilbert C*-module theory are still rather scattered through the literature.
		Characterize those C-algebras with the property that for every Hilbert* C-module over them and for each of its Hilbert* C*-submodules which coincides with its biorthogonal completion therein, the latter is always a topological direct summand of the former.
	www.imn.htwk-leipzig.de /~mfrank/hilmod.html (505 words)

	Amazon.ca: Books: Hilbert (Site not responding. Last check: 2007-10-21)
		And it illuminates the background of German social history against which the drama of Hilbert's life played...Beyond this, it is a poem in praise of mathematics." --This text refers to the Hardcover edition.
		Hilbert, who had retired in 1930 (retirement at age 68 was mandatory) was forced to watch as the work of decades was dismantled.
		Hilbert's life leads from the great days of the mid-nineteenth century to the Nazis and the atomic bomb.
	www.amazon.ca /exec/obidos/ASIN/0387049991 (903 words)

	Easy Fourier Analysis
		Hilbert Transform is not a particularly complex concept and can be much better understood if we take an intuitive approach first before delving into its formula which is related to convolution and is hard to grasp.
		The role of Hilbert transform as we can guess here is to take the carrier which is a cosine wave and create a sine wave out of it.
		Another way to write this definition is to recognize that Hilbert Transform is also the convolution of function 1/ pt with the signal g(t).
	www.complextoreal.com /tcomplex.htm (2446 words)

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