zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Riesz L p summability of spectral expansions related to the Schrödinger operator with constant magnetic field. (English) Zbl 1025.35012

The authors consider the Schrödinger operator with constant magnetic field

H=- j=1 d x j +ib j 2y j 2 + y j -ib j 2x j 2 -Δ l

in L p ( n ),n=2d+l, where Δ l is the Laplacian in l . Denote by E λ the spectral function of H. The Riesz summation operator of index β is defined as S λ β = 0 λ (1-t/λ) β dE t . It is proved that if β>max(n|1 p-1 2|-1 2,0) and |1 p-1 2|>1 n+1 then the operators S λ β are uniformly in λ bounded in L p and for any fL p ( n ),S λ β ff in L p ( n ).

Standard ingredients of the proof of Riesz summability (restriction estimate and kernel estimate) are also proved.

35P10Completeness of eigenfunctions, eigenfunction expansions for PD operators
35J10Schrödinger operator
35Q40PDEs in connection with quantum mechanics
47F05Partial differential operators