Let Tn be the linear Hadamard convolution operator acting over Hardy space H q , 1 ≤ q ≤ ∞. We call Tn a best approximation-preserving operator (BAP operator) if Tn(en) = en, where en(z) := z n , and if Tn(f ) q ≤ En(f )q for all f ∈ H q , where En(f )q is the best approximation by algebraic polynomials of degree a most n − 1 in H q space.We give necessary and sufficient conditions for Tn to be a BAP operator over H ∞ . We apply this result to establish an exact lower bound for the best approximation of bounded holomorphic functions. In particular, we show that the Landau-type inequality fn + c f N ≤ En(f )∞, where c > 0 and n < N , holds for every f ∈ H ∞ iff c ≤ 1 2 and N ≥ 2n + 1.
Abstract. The paper deals with the study of the innovation and investment provision of the environmental management development at industrial enterprises. The prerequisites for the environmental management development at the domestic enterprises are explained, including the development of the mechanism of international technological exchange and the scientific and technological progress, as well as international environmental safety programs. The classification of innovations in environmental management is theoretically substantiated for the following criteria: the field of activity (application); technological parameters; the degree of novelty; depending on the depth of the introduced changes; by the address principle. Innovative measures to raise environmental awareness among managers of domestic industrial enterprises are suggested; they are advanced training of employees of the enterprises in environmental management and involvement of external experts on environmental management who will conduct environmental consulting, environmental audits, environmental expertise, environmental outsourcing and franchising at the enterprise. The authors determined the main directions of the state policy of support for the innovation and investment activity in environmental management. They include providing legal, business and other services; assisting in finding partners; signing agreements under the state guarantee; creating specialized public research institutes, laboratories, centers of the environmentally oriented production development; implementing various programs aiming at enhancement of the innovative business promotion in the field of ecology within a single government program; making state orders for scientific and research activities, as well as and development and construction activities, which provide the initial demand for environmental innovations; stimulating innovative solutions of individual enterprises with the help of public financial institutions and other public authorities; performing tax reforms to encourage investors for long-term funding and crediting of investment projects; carrying out further improvement of property relations, privatization process and development of small and medium enterprises; carrying out environmental education, advertising, and promotion; creating a favorable investment climate for domestic and foreign investors. The paper presents substantiation of the advantages of the introduction of the investment and innovative model of development of industrial enterprises in providing environmental management. This will promote the positive image of the domestic industrial enterprises both on the domestic and foreign markets, the competitiveness of industrial products for environmentally sensible markets, the enhancement of investment attractiveness of industrial enterprises, and the innovative renovation of the production. Keywords: environmental management; innovation; investment; investment and innovation model; environmental innovations; industrial enterprise.Анотація. Робот...
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