Traces of functions of generalized Sobolev classes

Considering the Sobolev type function classes on a metric space equipped with a Borel measure we address the question of compactness of embeddings of the space of traces into Lebesgue spaces on the sets of less “dimension.” Also, we obtain compactness conditions for embeddings of the traces of the classical Sobolev spaces W _p ¹ on the “zero” cusp with a Hölder singularity at the vertex.     

Factorization of functions in generalized Nevanlinna classes

For functions in the classical Nevanlinna class analytic projection of produces where is the outer part of i.e., this projection factors out the inner part of . We show that if is area integrable with respect to certain measures on the disc, then the appropriate analytic projections of factor out zeros by dividing by a natural product which is a disc analogue of the classical Weierstrass product. This result is actually a corollary of a more general theorem of M. Andersson. Our contribution is to give a simple one complex variable proof which accentuates the connection with the Weierstrass product and other canonical objects of complex analysis.

     

Nonexistence of two classes of generalized bent functions

We obtain some new nonexistence results of generalized bent functions from \({\mathbb {Z}}^n_q\) to \({\mathbb {Z}}_q\) (called type [n, q]) in the case that there exist cyclotomic integers in \( {\mathbb {Z}}[\zeta _{q}]\) with absolute value \(q^{\frac{n}{2}}\). This result generalizes two previous nonexistence results \([n,q]=[1,2\times 7]\) of Pei (Lect Notes Pure Appl Math 141:165–172, 1993) and \([3,2\times 23^e]\) of Jiang and Deng (Des Codes Cryptogr 75:375–385, 2015). We also remark that by using a same method one can get similar nonexistence results of GBFs from \({\mathbb {Z}}^n_2\) to \({\mathbb {Z}}_m\).     

Closed classes generated by symmetric functions in the three-valued logic

Closed classes of functions in the three-valued logic whose generating systems consist of symmetric functions taking values in the set {0, 1} are studied in the paper. Criteria for the existence of a basis and for the existence of a finite basis are obtained for closed classes from the considered family.     

Approximation of certain classes of differentiable functions by generalized splines

We find the exnet value of the best (α, β)-approximation by generalized Chebyshev splines for a class of functions differentiable with weight on [?1, 1].     

Two classes of generalized functions used in nonlocal field theory

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space S⁰ (which is the Fourier transform of the Schwartz space ) and using test functions in the Gelfand-Shilov spaces S ⁰ . We prove that every functional defined on S⁰ has the same carrier cones as its restrictions to the smaller spaces S ⁰ . As an application of this result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular generalized functions of tempered growth and obtain the corresponding extension of Vladimirovs algebra of functions holomorphic in a tubular domain.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 2, pp. 195–210, May, 2005.     

Closed classes of the three-valued logic generated by systems containing symmetric functions

Closed classes of functions of the three-valued logic whose generating systems include nonmonotone symmetric functions taking values in the set {0, 1} are studied. It is shown that in some cases the problems of existence of a basis and existence of a finite basis can be reduced to similar problem for reduced generating systems.     

On the interrelation of the generalized Besov-Nikol'skii and Weyl-Nikol'skii classes of functions

, , , . .

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Dedicated to Professors K. Tandori and L. Leindler on the occasion of their anniversaries

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This work was completed in support of the Russian Foundation of Fundamental Research (Project # 96-01-00094) and of the International Scientific Foundation (Grant # NCI-300).     

Application of generalized Hadamard product on special classes of analytic univalent functions

In this paper, the author established certain results concerning the quasi-Hadamard product for generalized subclasses of univalent functions with positive coefficients.     

On closed sets of relational constraints and classes of functions closed under variable substitutions

Pippenger’s Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set A and taking values in a possibly different set B, where any or both of A and B may be finite or infinite. Received April 30, 2004; accepted in final form February 8, 2005.     

Closed orbits in homology classes

Dedicated to Pr. Akihiko Morimoto for his 60th birthday     

Generalized martingales,generalized Markov chains and generalized harmonic functions

Summary This paper introduces and studies a generalization of the notion of martingale which allows for a generalization of the concept of a Markov chain and a generalization of the concept of harmonic and superharmonic functions. The theory is supported by examples and techniques that suggest the natural character of the material developed.Deceased. Please address correspondence on Prof. Magda Peligrad; Department of Mathematical Sciences, University of Cincinnati, Mail Location 25, Cincinnati, OH 45221 USA     

On integral operators for certain classes of p-valent functions associated with generalized multiplier transformations

In this paper, we study new generalized integral operators for the classes of p-valent functions associated with generalized multiplier transformations.     

New classes of generalized monotonicity

This paper introduces new classes of generalized monotone functions and relates them to classes previously introduced.This work was supported by NSERC Grant A5789     

Embedding of classes of functions with bounded {\Phi}-variation into generalized Lipschitz spaces

In this note, sufficient and necessary conditions for embedding of classes \({\Phi}\)BV of functions with bounded \({\Phi}\)-variation in Schramm’s sense into generalized Lipschitz classes \({H_{q}^{\omega} (1 \leq q < \infty)}\) are obtained.