Search results for "Mathematical"
showing 10 items of 7967 documents
Bounds for Bessel functions
1989
We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.
Noether’s International School in Modern Algebra
2020
Pavel Alexandrov and Heinz Hopf met for the first time in Gottingen in the spring of 1926, soon after Alexandrov departed from Blaricum. Hopf had recently taken his doctorate in Berlin under Ludwig Bieberbach and Erhard Schmidt, and his research interests differed sharply from Alexandrov’s work in general topology.
Erzwingt die Quantenmechanik eine drastische Änderung unseres Weltbilds? Gedanken und Experimente nach Einstein, Podolsky und Rosen
1989
Von den Anfangen der Quantenmechanik bis heute gibt es Versuche, sie als statistische Theorie uber Ensembles individueller ‚klassischer’ Systeme zu interpretieren. Die Bedingungen, unter denen Theorien verborgener Parameter zu deterministischen Beschreibungen dieser individuellen Systeme als ‚klassisch’ angesehen werden konnen, wurden von Einstein, Podolsky und Rosen 1935 formuliert: 1. Physikalische Systeme sind im Prinzip separierbar. 2. Zu jeder physikalischen Grose, deren Wert man ohne Storung des betrachteten Systems mit Sicherheit voraussagen kann, existiert ein ihr entsprechendes Element der physikalischen Realitat. Zusammen sind sie, wie Bell 1964 gezeigt hat, prinzipiell unvertragl…
COMPLEX CONVEXITY AND VECTOR-VALUED LITTLEWOOD–PALEY INEQUALITIES
2003
Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.
Explicit expressions for Sturm-Liouville operator problems
1987
Throughout this paper H will denote a complex separable Hilbert space and L(H) denotes the algebra of all bounded linear operators on H. If T lies in L(H), its spectrum σ(T) is the set of all complex numbers z such zI–T is not invertible in L(H) and its compression spectrum σcomp(T) is the set of all complex numbers z such that the range (zI-T)(H) is not dense in H ([3, p. 240]). This paper is concerned with the Sturm–Liouville operator problemwhere λ is a complex parameter and X(t), Q, Ei, Fi for i = l,2, and t∈[0,a], are bounded operators in L(H). For the scalar case, the classical Sturm-Liouville theory yields a complete solution of the problem, see [4], and [7]. For the finite-dimension…
Mappings of finite distortion: Reverse inequalities for the Jacobian
2007
Let f be a nonconstant mapping of finite distortion. We establish integrability results on 1/Jf by studying weights that satisfy a weak reverse Holder inequality where the associated constant can depend on the ball in question. Here Jf is the Jacobian determinant of f.
Spectral Asymptotics for More General Operators in One Dimension
2019
In this chapter, we generalize the results of Chap. 3. The results and the main ideas are close, but not identical, to the ones of Hager (Ann Henri Poincare 7(6):1035–1064, 2006). We will use some h-pseudodifferential machinery, see for instance Dimassi and Sjostrand (Spectral Asymptotics in the Semi-classical Limit, London Mathematical Society Lecture Note Series, vol 268. Cambridge University Press, Cambridge, 1999).
Riesz-Fischer Maps, Semi-frames and Frames in Rigged Hilbert Spaces
2021
In this note we present a review, some considerations and new results about maps with values in a distribution space and domain in a σ-finite measure space X. Namely, this is a survey about Bessel maps, frames and bases (in particular Riesz and Gel’fand bases) in a distribution space. In this setting, the Riesz-Fischer maps and semi-frames are defined and new results about them are obtained. Some examples in tempered distributions space are examined.