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Este modulo nos dará una descripción de los espacios de Hilbert mas comunes y de sus propiedades básicas.

Espacios de hilbert comunes

A continuación veremos los cuatro Espacios de Hilbert mas comunes con los que usted tendráque tratar para la discusión y manipulación de señales y sistemas:

n (escalares reales ) y n (escalares complejos), también llamado 2 0 n 1

x x 0 x 1 x n - 1 Es una lista de números (secuencia finita). El producto interno para nuestros dos espacios son las siguientes:

  • Producto interno n :
    x y y x i 0 n 1 x i y i
  • Producto interno n :
    x y y x i 0 n 1 x i y i

Modelo para: Señal de tiempo discreto en el intervalo 0 n 1 o Señal Periódica (con periodo n ) de tiempo discreto. x 0 x 1 x n - 1

f L 2 a b es una función de energía finita en a b

Inner product

f g t a b f t g t
Modelo para: Señal de tiempo continuo en el intervalo a b o Señal Periódica (con periodo T b a ) de tiempo continuo

x 2 es una secuencia infinita de números que son cuadrados sumables

Producto interno

x y i x i y i
Modelo para: Señal no-periódica de tiempo discreto

f L 2 es una una función de energía finita en todo .

Producto interno

f g t f t g t
Modelo para: Señal no-periódica de tiempo continuo

AnÁLisis de fourier asociado

Cada uno de estos cuatro espacios de Hilbert tiene un análisis de Fourier asociado con el.

  • L 2 a b →Series de Fourier
  • 2 0 n 1 →Transformada Discreta de Fourier
  • L 2 →Transformada de Fourier
  • 2 →Transformada Discreta de Fourier en Tiempo
Pero los cuatros están basados en el mismo principio (Espacio de Hilbert).
no todos los espacios normalizados son espacios de Hilbert
Por ejemplo: L 1 ( ) , 1 f t f t . trate como usted pueda, de encontrar el producto interno que induce esta norma, es decir...tal que: · · such that
f f t f t 2 2 1 f 2
De echo, para todo el espacio L p , L 2 es el único que es un espacio de Hilbert.

Los espacios de Hilbert son en gran medida los más agradables, si se usa o estudia la expansión de bases ortonormales entonces usted empezara a ver por que esto es cierto.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Señales y sistemas. OpenStax CNX. Sep 28, 2006 Download for free at http://cnx.org/content/col10373/1.2
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