| 1. |
- Aleman, Alexandru, et al.
(författare)
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Weighted conformal invariance of Banach spaces of analytic functions
- 2021
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 280:9
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Tidskriftsartikel (refereegranskat)abstract
- We consider Banach spaces of analytic functions in the unit disc which satisfy a weighted conformal invariance property, that is, for a fixed α>0 and every conformal automorphism φ of the disc, f→f∘φ(φ′)α defines a bounded linear operator on the space in question, and the family of all such operators is uniformly bounded in operator norm. Many common examples of Banach spaces of analytic functions like Korenblum growth classes, Hardy spaces, standard weighted Bergman and certain Besov spaces satisfy this condition. The aim of the paper is to develop a general approach to the study of such spaces based on this property alone. We consider polynomial approximation, duality and complex interpolation, we identify the largest and the smallest as well as the “unique” Hilbert space satisfying this property for a given α>0. We investigate the weighted conformal invariance of the space of derivatives, or anti-derivatives with the induced norm, and arrive at the surprising conclusion that they depend entirely on the properties of the (modified) Cesàro operator acting on the original space. Finally, we prove that this last result implies a John-Nirenberg type estimate for analytic functions g with the property that the integration operator f→∫0zf(t)g′(t)dt is bounded on a Banach space satisfying the weighted conformal invariance property.
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| 2. |
- Chuaqui, Martin, et al.
(författare)
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On the convolution of convex 2-gons
- 2024
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier. - 0022-247X .- 1096-0813. ; 538:2
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Tidskriftsartikel (refereegranskat)abstract
- We study the convolution of functions of the form [Formula presented] which map the open unit disk of the complex plane onto polygons of 2 edges when α∈(0,1). Inspired by a work of Cima, we study the limits of convolutions of finitely many fα and the convolution of arbitrary unbounded convex mappings. The analysis for the latter is based on the notion of angle at infinity, which provides an estimate for the growth at infinity and determines whether the convolution is bounded or not. A generalization to an arbitrary number of factors shows that the convolution of n randomly chosen unbounded convex mappings has a probability of 1/n! of remaining unbounded. We provide the precise asymptotic behavior of the coefficients of the functions fα.
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| 3. |
- Hefzi, Hooman, et al.
(författare)
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Multiplex genome editing eliminates the Warburg Effect without impacting growth rate in mammalian cells
- 2024
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The Warburg effect is ubiquitous in proliferative mammalian cells, including cancer cells, but poses challenges for biopharmaceutical production, as lactate accumulation inhibits cell growth and protein production. Previous efforts to eliminate lactate production via knockout have failed in mammalian bioprocessing since lactate dehydrogenase has proven essential. However, here we eliminated the Warburg effect in Chinese hamster ovary (CHO) and HEK293 cells by simultaneously knocking out lactate dehydrogenase and regulators involved in a negative feedback loop that typically inhibits pyruvate conversion to acetyl-CoA. In contrast to long-standing assumptions about the role of aerobic glycolysis, Warburg-null cells maintain wildtype growth rate while producing negligible lactate. Further characterization of Warburg-null CHO cells showed a compensatory increase in oxygen consumption, a near total reliance on oxidative metabolism, and higher cell densities in fed-batch cell culture. These cells remained amenable for production of diverse biotherapeutic proteins, reaching industrially relevant titers and maintaining product glycosylation. Thus, the ability to eliminate the Warburg effect is an important development for biotherapeutic production and provides a tool for investigating a near-universal metabolic phenomenon.
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