The main requirements for obtaining the Italian citizenship recognition are the following:

the applicant should have an ascendant with Italian origin, who has never requested the naturalization in another foreign country or has requested it after the birth of the applicant;
That being said, the procedure for obtaining the recognition of the Italian citizenship consists of the following steps:

Collect of all the relevant documents illustrating the whole bloodline between the Italian ascendant and the applicant (e.g. birth, marriage and death certificate of the ascendant), In case the applicant resides abroad, the request shall be submitted to the competent Italian Embassy or Consulate in the jurisdiction in which the applicant is resident;
In case the applicant resides in Italy, the request shall be submitted to the competent Italian Municipality in the jurisdiction in which the applicant is resident;
Issue of the decree containing the recognition of the Italian citizenship, after the conduct of duly investigations by the competent Italian authority.

The Investor VISA, or so-called Golden VISA, has been introduced by Italian law in 2016 in order to attract foreign investments in Italy. In particular if you are an investor, this specific regulation, within immigration law, allows you the entrance and the accommodation in Italy for periods exceeding three months, outside the quotas system. This is possible if you make:

an investment of at least € 2.000.000,00 in securities issued by the Italian government;
an investment of at least € 500.000,00 in equity instruments of a company incorporated and operating in Italy;
an investment of at least € 250.000,00 into an existing Italian innovative start-up company; or
a philanthropic donation of at least € 1.000.000,00 to support a public interest project, in the fields of culture, education, immigration management, scientific research, recovery of cultural and landscape assets.
Therefore, an investment in a non-regulated Italian limited liability company that will carry out activities like the acquisition of interests, shares, shareholdings in other companies or assets, would be considered a valid investment that meets the Investor Visa requirement.

Civil status documents (e.g. birth, marriage and death certificate) in full form copy, duly translated into Italian and apostilled in the jurisdiction in which the applicant is resident (or notarized and legalized with an Italian Embassy or Consulate if the jurisdiction where the applicant is resident is not a member of the apostille convention) related to whole chain which connect the applicant with the Italian ascendant;
Certificate of foreign non-naturalization of the Italian ascendant or his/her certificate of naturalization with date of acquisition of the foreign citizenship or copy of the judgment of foreign naturalization indicating the date of oath;
In case the applicant resides in Italy, certificate of residence registration to the Italian Municipality.

The Italian government has recently implemented a tax package and fast-track VISA
procedure to attract wealthy individuals that want to relocate to Italy.
This package includes a € 100,000 flat tax on all foreign income for individuals who become
Italian resident after at least a 9-year period of residence outside of Italy.
The tax package is integrated by a fast-track visa procedure for investors and their relative

The Elective Residency Visa allows to a third-country national who is able to maintain itself autonomously, to stay in Italy without work.

Who can apply for it?
A third-country national who has a regular personal income that derives from retirement or annuity, real estate properties, the ownership of stable commercial economic activities or other economic resources different from the employment. In any of these cases, the resources must not be less of € 31.159,29 per year.

Which benefits does it have?
This kind of visa can be issued also for family members such as cohabiting spouse, minor children and adult dependent children. However, the abovementioned financial resources must be considered sufficient also for them. In particular, in case of application also for cohabiting spouse the monthly amount to be demonstrated must be increased of at least 20%. This increase must be of at least 5% for each applicant child.

How can I apply for it?
The application must be submitted to the competent Italian diplomatic authority in your Country of residence. In order to do it, you should take an appointment and be present in person.

Which documents do I need to apply?
The listed documents must be submitted the day of the appointment, in order to apply for the Elective Residency Visa:

Application form, duly filled;
Recent photo in card format;
Valid travel document expiring at least three months longer than the required visa;
Certification stating broad, autonomous, stable and regular economic resources, whose continuity over time can be reasonably assumed, coming from sources other than subordinate work. In order to demonstrate these stable resources, you can produce:
proof of receiving annuities in Italy or in the Country of origin;
proof of purchase of real estate or preliminary sale contract;
proof of ownership of real estate in the Country of origin;
proof of receiving annuities in the Country of origin;
proof of the conclusion of a real estate affair that states the actual possibility of earning income
Health insurance with a minimum coverage of € 30.000,00 for emergency hospitalization expenses and repatriation costs, valid throughout the Schengen area;
Availability of an accommodation to be elected for residence, such as property or rented with a contract already signed.
Please consider that this kind of long-term visa is in any case remitted to the discretion of the different consular representations, in relation to the quantum of the attested resources and their presumable stay in the future.