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reproducin

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There are 10 letters in REPRODUCIN ( C³D²E¹I¹N¹O¹P³R¹U¹ )

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CEP COD CON COP COR CRU CUD CUE CUP CUR DEN DIE DIN DIP DOC DOE DON DOR DUE DUI DUN DUO DUP ECU END EON ERN ERR ICE ION IRE NIP NOD NOR ODE ONE OPE ORC ORE OUD OUR PEC PED PEN PER PIC PIE PIN PIU POD POI PRO PUD PUN PUR REC RED REI REP RID RIN RIP ROC ROD ROE RUE RUN UDO UPO URD URN URP

2 letters out of REPRODUCIN

DE DO ED EN ER ID IN NE NO NU OD OE OI ON OP OR PE PI RE UN UP

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Definitions of reproducin in various dictionaries:

REPRODUCIN - In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation...

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Reproducin might refer to
In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions * * * * f * * * {\displaystyle f} * and * * * * g * * * {\displaystyle g} * in the RKHS are close in norm, i.e., * * * * ‖ * f * − * g * ‖ * * * {\displaystyle \\|f-g\\|} * is small, then * * * * f * * * {\displaystyle f} * and * * * * g * * * {\displaystyle g} * are also pointwise close, i.e., * * * * * \| * * f * ( * x * ) * − * g * ( * x * ) * * \| * * * * {\displaystyle \|f(x)-g(x)\|} * is small for all * * * * x * * * {\displaystyle x} * . The reverse need not be true. * It is not entirely straightforward to construct a Hilbert space of functions which is not an RKHS. Note that L2 spaces are not Hilbert spaces of functions (and hence not RKHSs), but rather Hilbert spaces of equivalence classes of functions (for example, the functions * * * * f * * * {\displaystyle f} * and * * * * g * * * {\displaystyle g} * defined by * * * * f * ( * x * ) * = * 0 * * * {\displaystyle f(x)=0} * and * * * * g * ( * x * ) * = * * 1 * * * Q * * * * * * {\displaystyle g(x)=1_{\mathbb {Q} }} * are equivalent in L2). However, there are RKHSs in which the norm is an L2-norm, such as the space of band-limited functions (see the example below). * An RKHS is associated with a kernel that reproduces every function in the space in the sense that for any * * * * x * * * {\displaystyle x} * in the set on which the functions are defined, "evaluation at * * * * x * * * {\displaystyle x} * " can be performed by taking an inner product with a function determined by the kernel. Such a reproducing kernel exists if and only if every evaluation functional is continuous. * The reproducing kernel was first introduced in the 1907 work of Stanisław Zaremba concerning boundary value problems for harmonic and biharmonic functions. James Mercer simultaneously examined functions which satisfy the reproducing property in the theory of integral equations. The idea of the reproducing kernel remained untouched for nearly twenty years until it appeared in the dissertations of Gábor Szegő, Stefan Bergman, and Salomon Bochner. The subject was eventually systematically developed in the early 1950s by Nachman Aronszajn and Stefan Bergman.These spaces have wide applicatio...

Reproducin might refer to

In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions
*
*
*
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* and
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* in the RKHS are close in norm, i.e.,
*
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* ‖
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* −
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*
*
* {\displaystyle \|f-g\|}
* is small, then
*
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* {\displaystyle f}
* and
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* g
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* {\displaystyle g}
* are also pointwise close, i.e.,
*
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* {\displaystyle |f(x)-g(x)|}
* is small for all
*
*
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* {\displaystyle x}
* . The reverse need not be true.
* It is not entirely straightforward to construct a Hilbert space of functions which is not an RKHS. Note that L2 spaces are not Hilbert spaces of functions (and hence not RKHSs), but rather Hilbert spaces of equivalence classes of functions (for example, the functions
*
*
*
* f
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* {\displaystyle f}
* and
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* defined by
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* {\displaystyle g(x)=1_{\mathbb {Q} }}
* are equivalent in L2). However, there are RKHSs in which the norm is an L2-norm, such as the space of band-limited functions (see the example below).
* An RKHS is associated with a kernel that reproduces every function in the space in the sense that for any
*
*
*
* x
*
*
* {\displaystyle x}
* in the set on which the functions are defined, "evaluation at
*
*
*
* x
*
*
* {\displaystyle x}
* " can be performed by taking an inner product with a function determined by the kernel. Such a reproducing kernel exists if and only if every evaluation functional is continuous.
* The reproducing kernel was first introduced in the 1907 work of Stanisław Zaremba concerning boundary value problems for harmonic and biharmonic functions. James Mercer simultaneously examined functions which satisfy the reproducing property in the theory of integral equations. The idea of the reproducing kernel remained untouched for nearly twenty years until it appeared in the dissertations of Gábor Szegő, Stefan Bergman, and Salomon Bochner. The subject was eventually systematically developed in the early 1950s by Nachman Aronszajn and Stefan Bergman.These spaces have wide applicatio...

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reproducin

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There are 10 letters in REPRODUCIN ( C3D2E1I1N1O1P3R1U1 )

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