September 2, 2017

Download Analysis of the Hodge Laplacian on the Heisenberg group by Detlef Muller, Marco M. Peloso, Fulvio Ricci PDF

By Detlef Muller, Marco M. Peloso, Fulvio Ricci

ISBN-10: 1470409399

ISBN-13: 9781470409395

The authors ponder the Hodge Laplacian ? at the Heisenberg team H n , endowed with a left-invariant and U(n) -invariant Riemannian metric. For 0=k=2n 1 , allow ? ok denote the Hodge Laplacian constrained to okay -forms. during this paper they tackle 3 major, similar questions: (1) no matter if the L 2 and L p -Hodge decompositions, 1 (2) no matter if the Riesz transforms d? -12 okay are L p -bounded, for 1<<8 ; (3) the right way to end up a pointy Mihilin-Hormander multiplier theorem for ? ok , 0=k=2n 1

Show description

Read Online or Download Analysis of the Hodge Laplacian on the Heisenberg group PDF

Similar analysis books

Introduction to Real Analysis (4th Edition)

This article offers the basic options and methods of actual research for college students in all of those components. It is helping one increase the facility to imagine deductively, examine mathematical events and expand principles to a brand new context. just like the first 3 variants, this variation keeps a similar spirit and ordinary technique with addition examples and enlargement on Logical Operations and Set idea.

Methods and Supporting Technologies for Data Analysis

Including the advance of knowledge applied sciences the necessities for information research instruments have grown considerably. because of such fresh advances, as ubiquitous computing or the web of items, facts modeling, administration and processing develop into progressively more hard projects. clients are looking to get whole wisdom from huge quantity of information of other varieties and codecs in all attainable environments.

Additional resources for Analysis of the Hodge Laplacian on the Heisenberg group

Example text

D. From the previous results we immediately get an explicit formula for U2, , at least when p = 0 and q = 0. However, if p = 0 or q = 0, our formulas, when properly interpreted, persist, and we obtain the following result: Recall that if p = 0, then X p,q = (I − C)X p,q , and if q = 0, then Y p,q = (I − C)Y p,q . Let us correspondingly put r so that r if p ≥ 1, if p = 0, = r is always invertible on X p,q , and if q ≥ 1, if q = 0, = r on Y p,q . 12. 10. 9. 13. 12 maps the space Z p,q onto V2,p,q and intertwines D := Δ0 + i(q − p)T + ( + 1)(n − k + + 1) with Δk p,q on the core.

M. PELOSO, and F. RICCI 50 In particular, if we know that A∗ A maps D1 into H1 , then A∗1 A1 ξ = A∗ Aξ for every ξ ∈ D1 . Proof. Since A(D1 ) ⊂ E1 , it suffices to prove that A∗1 = PH1 A∗ on E1 . But, if x ∈ D1 ⊂ dom A1 , ξ ∈ E1 ⊂ dom A∗1 , then x, A∗1 ξ = A1 x, ξ = Ax, ξ = x, A∗ ξ = x, PH1 A∗ ξ . This implies that A∗1 ξ = PH1 A∗ ξ, since D1 is dense in H1 . D. 1. A unitary intertwining operator for V0p,q We recall from the preceding discussion that the intertwining operator on V0p,q is Φ, which reduces to the identity on this space.

D. 9. 7) maps W0p,q , respectively Ξp,q , onto and intertwines D± with Δk on the core. + − Moreover, U1, : W0p,q → L2 Λk and U1, : Ξp,q → L2 Λk are linear isometries p,q,+ p,q,− onto their ranges V1, and V1, , respectively, which intertwine D+ resp. 17) Δk V p,q,± 1, ± ± −1 = U1, D± (U1, ) on dom Δk . V p,q,± 1, ± −1 ± ) denotes the inverse of U1, when viewed as an operator into its Here, (U1, p,q,± range V1, . ± Finally, if we regard of U1, as an operator mapping into L2 Λk , then P1,± := p,q,± ± ± ∗ P1,p,q,± := U1, (U1, ) is the orthogonal projection from L2 Λk onto V1, .

Download PDF sample

Rated 4.51 of 5 – based on 23 votes