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**Juan Jose Molina Gonzalez ^{*}**

Department of Mathematics, Autonomous University of Madrid, Madrid, Spain

- *Corresponding Author:
- Juan Jose Molina Gonzalez

Department of Mathematics,

Autonomous University of Madrid,

Madrid,

Spain;

**Email:**jjmg@um.es

**Received: **09-Nov-2022, Manuscript No. JSMS-22-79385; **Editor assigned: **12-Nov-2022, Pre QC No. JSMS-22-79385 (PQ); **Reviewed: **26-Nov-2022, QC No. JSMS-22-79385; **Revised: **16-Feb-2023, Manuscript No. JSMS-22-79385 (R); **Published: **24-Feb-2023, DOI: 10.4172/JSMS.9.1.001

**Citation:** Gonzalez JJM. K-Frames in Terms of Descomposition of Operators-Hilbert Operators. RRJ Stats Math Sci. 2023;09:001.

**Copyright:** © 2023 Gonzalez JJM. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

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Suppose a compact n-manifold M admits a topological non-degenerate function of such that all the critical points off of index λ lie at the level λ. Then M admits a cell decomposition with exactly as many cells of dimension λ as f has critical points of index λ, illustrates some of the difficulties in the theory of topological non-degenerate functions. If (α,b) is an interval of regular values of a C+ In numerique mathematics a[α, b] is an interval of regular values of a C+-α Hilbert operators in terms of descomposition of this smooths polinomials function that create n manifolds of ranks r=0,1........,n in a closed form of M manifold presented K-frames in Labelian groups that are descomposed in others smooths functions of minor rank subgroups of C in that the at G+(Hy^ Gx) (^*G;), direct sum (complete direct sum) and in the form Hom (U,V) group of homomorphisms of U into V End G group of endomorphism of G Ext (L,K) group of extensions of K by L in a formed group α Hilbert operators of descomposition and Div (U,V) divisible U into V group subgroup. in GL(n,K). It is if σ Hilbert operator is nontrivial, then is ϕ necessarily another automorphism of K(n,X) If σ is a nonzero complex number, then σ=|σ|eiθ for some real number θ then σ Hilbert operator is a in equivoque 20 automorphisme of K(n,X)This theorem of algebra analysis by Hilbert operators sum in a direct sum group and subgroup in the form describe ateriorerly for operators in L(θ, H), a similar decomposition. The choice for eiθ would be the citrateautomorphisme of K(n,X).

Be a Labelian group of rank r=0,1. n in a closed form the definition that is building in the form integer of (log0..log2,. Logn) tend to a closed moduli form that is lim tend to 0, in that the at the torus Tn tend to close in a zero log 0 point. For modular cusp forms of even weight the Anne Eischler integral determines for a given modular cusp form of even positive weight a cohomology (rank r=0. n) class with values transformed smooths polinomials functions.

Weight of the given cusp form of modular form is done by precisement this closed forms such G=SL2(n,R), H=G/H in the torus or moduli form Γ(1)=SL2(n,R) by a rank=1 and transformed smooths polinomial function log 0 that is a modular form or in that the at a Labeling semi group 34 When 0=1 be a modular form is definited in G=SL2(n,R), H=G/H Labeling groups of a closed form done by Eschler integer by rank r=0.......n in form form Γ(n)=SL2(n, R) by projective surfaces on a L x L cycle over K or Γ(1)=SL2(n,R) Shimura varieties can be represented some and isomorphism of G3(A1,3)n in R2(L, n) is in general a Langlands established of such form on LAbelian Semejant to flowed by classic a quantum system Poisson system partial differential 41 equations moves in G-3 in a hyperbolicity G-spectra on a simplectic manifold of a L-3 form Lie Abelian dynamical hyperplanes or modular curves thatconformed a Langland respectively on a Labelian varieties GL2(n, ç) or GL3(n,ç) a simplectic manifold degenerateon L-2 or no degenerate in L-3 in a Geodesic map in the last (Being ç a 45 simplectic space).

A Shimura variety is a higher dimensional n of M manifold following the first citrate notation analogue of Hermitian simetric of smooth functions of rank r=(n,0,1,2,......n) that arises as a quotient Lie Abelian dynamical hyperplanes or modular curves that conformed a Langland respectively on a Labelian varieties It is a particular case of a Langland manifold that in dynamical midnest nastwest carries a k-4 in this example or in a simple case a K-3 on a simplectic manifold of L-4 form Labelian or L-3 respectively. Hilbert spaces and Siegel spaces are particular cases of Shimura varieties, Hilbert spaces on L-3 Labelian and Siegel space in a most higher dimensional space.