Otto Blumenthal (1876–1944) in retrospect

Butzer, Paul L.; Volkmann, Lutz

doi:10.1016/j.jat.2005.09.013

Cited by 10 publications

(12 citation statements)

References 79 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As in [14, §3], we can establish by induction on s that all series on the right-hand side of (11) converge for every fixed value of n with n ν 1 , where ν 1 is defined in (5), in view of condition (2). More, it can be proved that E s (n) f s for n ν 1 , the sequence of constants {f s } ∞ s=0 being recursively defined by…”

Section: Proof Looking For a Solution Of The Formmentioning

confidence: 90%

“…for every S > 1 and k > ν 1 , since V n decreases with n. The last term on the right-hand side of (16) is summable (as a function of k) by condition (2). An estimate can also be obtained for the first differences, E n .…”

Section: Proof Looking For a Solution Of The Formmentioning

confidence: 98%

“…When both conditions, (2) and (6), hold, the pair ({Y (1) n }, {Y (2) n }) generates the right-module of solutions to Eq. (1) with A > 0, for n μ.…”

Section: The Case Of An Asymptotically Positive Coefficientmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic approximations for second-order linear difference equations in Banach algebras, II

Soldà

Spigler

Vianello

2008

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

A Liouville-Green (WKB) asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras. The special case of linear matrix difference equations (or, equivalently, of second-order systems) is emphasized. Rigorous and explicitly computable bounds for the error terms are obtained, and this when both, the sequence index and some parameter that may enter the coefficients, go to infinity. A simple application is made to orthogonal matrix polynomials in the Nevai class.

show abstract

Section: Proof Looking For a Solution Of The Formmentioning

confidence: 90%

Section: Proof Looking For a Solution Of The Formmentioning

confidence: 98%

See 1 more Smart Citation

Asymptotic approximations for second-order linear difference equations in Banach algebras, II

Soldà

Spigler

Vianello

2008

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Recent studies concerned the life and work of Otto Blumenthal [30] and Herbert Raabe's work in multiplex signal transmission [11]. Together with Jean Mawhin we are now completing vol.…”

Section: History Of Mathematics and Conclusionmentioning

confidence: 99%

A retrospective on 60 years of approximation theory and associated fields

Butzer

2009

Journal of Approximation Theory

View full text Add to dashboard Cite

In collecting material for an autobiographical statement, I realized that I had been privileged to experience and participate in the emergence and evolution of approximation theory across some 60 years. As a student and then as a professional, I had observed the several strands of development within this exciting enterprise. As the son of a German emigré family, in England and Canada, I was schooled on two continents, comfortable with three languages, and exposed to a world of cultural contrasts. In my studies at Toronto (1948Toronto ( -1951, I was exposed to expatriate lecturers who had worked with the British and Russian pioneers in Fourier analysis and approximation. The Cambridge lecturing and tutoring style that permeated Toronto at the time also had a lifelong impact on my classroom presence and above all, my challenging and nurturing relationship with several generations of students.After a first position at McGill University, I spent some time in Paris and then 2 years in Mainz, where I had very productive interactions with German and US mathematicians. After semester stays in Freiburg and Würzburg, I took up a position at the Aachen University of Technology in 1958, at a time when the mathematics department was expanding its program and mission. After my promotion to chair professor in 1962, my research was diversifying and I was training my first doctoral students.Convinced of the importance of international and collaborative scholarship, I organized a first international symposium at the Oberwolfach Conference Center in August 1963. It was, perhaps unexpectedly, successful and was followed by seven further conferences across 20 years. In all, these Oberwolfach symposia-with Béla Szőkefalvi-Nagy as co-organizer from the fourth onwards-drew about 250 different experts from 24 countries including Hungary, Bulgaria, Poland, Roumania and eventually Russia, the roster of participants almost representing a Who's Who in approximation theory and associated fields such as harmonic analysis, functional analysis and operator theory, integral transform theory, orthogonal polynomials, interpolation, special functions, divergent series. The scope of the contacts so facilitated served to weaken national controls over research, favoring the emergence of new clusters of specialists, with partially overlapping interests, all thriving with the heightened interchange of ideas, methods and goals. The symposia and new research

show abstract

“…The couple were victims of the Nazi Holocaust. 7 Wilhelm's son Erich, born in 1880, was a doctor, a collector, a bibliophile, and the author of more than 500 publications on the histories of medicine and literature. He and his wife had 2 children.…”

Section: Subsequent Historymentioning

confidence: 99%

The Two Anomalies of Wilhelm Ebstein

Mazurak¹,

Kusa²

2017

Texas Heart Institute Journal

View full text Add to dashboard Cite

The year 2016 was the 180th anniversary of Wilhelm Ebstein's birth and the 150th anniversary of his description of the congenital tricuspid valve malformation that came to be known as Ebstein anomaly. We present a brief history of the life and work of Dr. Wilhelm Ebstein. Despite his distinguished career, he is seemingly forgotten in his own birthplace. We include a review of the relevant historical medical literature.

show abstract

Otto Blumenthal (1876–1944) in retrospect

Cited by 10 publications

References 79 publications

Asymptotic approximations for second-order linear difference equations in Banach algebras, II

Asymptotic approximations for second-order linear difference equations in Banach algebras, II

A retrospective on 60 years of approximation theory and associated fields

The Two Anomalies of Wilhelm Ebstein

Contact Info

Product

Resources

About