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Keywords = vector-valued tempered distributions

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17 pages, 3220 KiB  
Article
Seasonal Dynamics of Culturable Yeasts in Ornithogenically Influenced Soils in a Temperate Forest and Evaluation of Extracellular Enzyme Secretion in Tausonia pullulans at Different Temperatures
by Anna Glushakova, Anna Sharova and Aleksey Kachalkin
J. Fungi 2024, 10(8), 532; https://doi.org/10.3390/jof10080532 - 30 Jul 2024
Viewed by 1654
Abstract
The culturable yeast communities in temperate forest soils under the ornithogenic influence were studied in a seasonal dynamic. To investigate the intense ornithogenic influence, conventional and “live” feeders were used, which were attached to trees in the forest and constantly replenished throughout the [...] Read more.
The culturable yeast communities in temperate forest soils under the ornithogenic influence were studied in a seasonal dynamic. To investigate the intense ornithogenic influence, conventional and “live” feeders were used, which were attached to trees in the forest and constantly replenished throughout the year. It was found that the yeast abundance in the soil under strong ornithogenic influence reached the highest values in winter compared to the other seasons and amounted to 4.8 lg (cfu/g). This was almost an order of magnitude higher than the minimum value of yeast abundance in ornithogenic soils determined for summer. A total of 44 yeast species, 21 ascomycetes and 23 basidiomycetes, were detected in ornithogenic soil samples during the year. These included soil-related species (Barnettozyma californica, Cyberlindnera misumaiensis, Cutaneotrichosporon moniliiforme, Goffeauzyma gastrica, Holtermanniella festucosa, Leucosporidium creatinivorum, L. yakuticum, Naganishia adeliensis, N. albidosimilis, N. globosa, Tausonia pullulans, and Vanrija albida), eurybionts (yeast-like fungus Aureobasidium pullulans, Debaryomyces hansenii, and Rhodotorula mucilaginosa), inhabitants of plant substrates and litter (Cystofilobasidium capitatum, Cys. infirmominiatum, Cys. macerans, Filobasidium magnum, Hanseniaspora uvarum, Metschnikowia pulcherrima, and Rh. babjevae) as well as a group of pathogenic and opportunistic yeast species (Arxiozyma bovina, Candida albicans, C. parapsilosis, C. tropicalis, Clavispora lusitaniae, and Nakaseomyces glabratus). Under an ornithogenic influence, the diversity of soil yeasts was higher compared to the control, confirming the uneven distribution of yeasts in temperate forest soils and their dependence on natural hosts and vectors. Interestingly, the absolute dominant species in ornithogenic soils in winter (when the topsoil temperature was below zero) was the basidiomycetous psychrotolerant yeast T. pullulans. It is regularly observed in various soils in different geographical regions. Screening of the hydrolytic activity of 50 strains of this species at different temperatures (2, 4, 10, 15 and 20 °C) showed that the activity of esterases, lipases and proteases was significantly higher at the cultivation temperature. Ornithogenic soils could be a source for the relatively easy isolation of a large number of strains of the psychrotolerant yeast T. pullulans to test, study and optimize their potential for the production of cold-adapted enzymes for industry. Full article
(This article belongs to the Special Issue Diversity and Biotechnology of Soil Fungi and Rhizosphere Fungi)
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11 pages, 289 KiB  
Article
Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values
by Richard D. Carmichael
Axioms 2023, 12(11), 1036; https://doi.org/10.3390/axioms12111036 - 6 Nov 2023
Viewed by 1439
Abstract
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1p<2, if the boundary value is in the vector-valued [...] Read more.
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1p<2, if the boundary value is in the vector-valued Lp,1p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2p. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1p. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
14 pages, 323 KiB  
Article
Cauchy Integral and Boundary Value for Vector-Valued Tempered Distributions
by Richard D. Carmichael
Axioms 2022, 11(8), 392; https://doi.org/10.3390/axioms11080392 - 10 Aug 2022
Cited by 2 | Viewed by 1607
Abstract
Using the historically general growth condition on scalar-valued analytic functions, which have tempered distributions as boundary values, we show that vector-valued analytic functions in tubes TC=Rn+iC obtain vector-valued tempered distributions as boundary values. In a certain [...] Read more.
Using the historically general growth condition on scalar-valued analytic functions, which have tempered distributions as boundary values, we show that vector-valued analytic functions in tubes TC=Rn+iC obtain vector-valued tempered distributions as boundary values. In a certain vector-valued case, we study the structure of this boundary value, which is shown to be the Fourier transform of the distributional derivative of a vector-valued continuous function of polynomial growth. A set of vector-valued functions used to show the structure of the boundary value is shown to have a one–one and onto relationship with a set of vector-valued distributions, which generalize the Schwartz space DL2(Rn); the tempered distribution Fourier transform defines the relationship between these two sets. By combining the previously stated results, we obtain a Cauchy integral representation of the vector-valued analytic functions in terms of the boundary value. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory)
24 pages, 390 KiB  
Article
Generalized Vector-Valued Hardy Functions
by Richard D. Carmichael
Axioms 2022, 11(2), 39; https://doi.org/10.3390/axioms11020039 - 20 Jan 2022
Cited by 3 | Viewed by 2396
Abstract
We consider analytic functions in tubes Rn+iBCn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone [...] Read more.
We consider analytic functions in tubes Rn+iBCn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone in Rn, an open convex cone in Rn, and a regular cone in Rn, with this latter cone being an open convex cone which does not contain any entire straight lines. The analytic functions satisfy several different growth conditions in Lp norm, and all of the resulting spaces of analytic functions generalize the vector valued Hardy space Hp in Cn. The analytic functions are represented as the Fourier–Laplace transform of certain vector valued Lp functions which are characterized in the analysis. We give a characterization of the spaces of analytic functions in which the spaces are in fact subsets of the Hardy functions Hp. We obtain boundary value results on the distinguished boundary Rn+i{0¯} and on the topological boundary Rn+iB of the tube for the analytic functions in the Lp and vector valued tempered distribution topologies. Suggestions for associated future research are given. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory)
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